If you are interested in participating in our gong show with a 10 minutes talk, please apply here: https://forms.gle/qZhenC2933xJSjQB9
Titles and abstracts for the fifth Gong Show
Meer Ashwinkumar, "Three-dimensional WZW model and the R-matrix of the Yangian"
We study four-dimensional Chern-Simons theory on D×C (where D is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model. This boundary theory gives rise to a current algebra that turns out to be an "analytically-continued" toroidal Lie algebra. In addition, we show how certain bulk correlation functions of two and three Wilson lines can be captured by boundary correlation functions of local operators in the three-dimensional WZW model. In particular, we reproduce the leading and subleading nontrivial contributions to the rational R-matrix purely from the boundary theory. Based on JHEP 02 (2021) 227.
Carlos Bercini, "The Wilson Loop - Large Spin OPE dictionary"
We work out the map between null polygonal hexagonal Wilson loops and spinning three point functions in large N conformal gauge theories by mapping the variables describing the two different physical quantities and by working out the precise normalization factors entering this duality. By fixing all the kinematics we open the ground for a precise study of the dynamics underlying these dualities – most notably through integrability in the case of planar maximally supersymmetric Yang-Mills theory.
Based on: arXiv:2110.04364 with Vasco Gonçalves, Alexandre Homrich, Pedro Vieira.
Aleix Gimenez-Grau, "Bootstrapping holographic defect correlators"
We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in N=4 SYM. We use inversion formula technology in order to reconstruct the CFT data starting from a single discontinuity of the correlator. In the planar strong coupling limit only a finite number of conformal blocks contributes to the discontinuity, which allows us to obtain elegant closed-form expressions for two-point functions of single-trace operators of weight J=2,3,4 . Our final result passes a number of non-trivial consistency checks: it has the correct discontinuity, it satisfies the superconformal Ward identities, it has a sensible expansion in both defect and bulk OPEs, and is consistent with available results coming from localization. The method is completely algorithmic and can be implemented to calculate correlators of arbitrary weight.
Himanshu Khanchandani, "CFT in AdS and Gross-Neveu BCFT"
I will start by describing how studying a CFT in AdS can give us non-trivial information about the corresponding BCFT on half space. Then I will use this idea to study Gross-Neveu BCFT. I will discuss various boundary phases for the large N Gross-Neveu model and show what they correspond to in an epsilon expansion description in d = 2 + epsilon and 4 - epsilon dimensions. Based on https://arxiv.org/abs/2110.04268.
Levente Pristyák, "Current operators in the XYZ model"
In recent years, Generalized Hydrodynamics (GHD) was developed to describe the Euler-scale transport properties of integrable systems. However, GHD so far was applied only to models with a global U(1) symmetry, leading to particle conservation. But the current operators, that describe the flow of the conserved charges can be defined even in the absence of particle conservation, and therefore can serve as the basis of a GHD setup. A well-known example of a model lacking U(1) symmetry is the XYZ spin chain. In my talk I present an ongoing investigation of the current operators and their mean values in this model, using a generalized Algebraic Bethe Ansatz.
Xinyu Zhang, "Hidden symmetry in 4d N=2 quiver gauge theory"
We study the global symmetry of 4d N=2 superconformal quiver gauge theory, which can be obtained from the orbifold projection of the N=4 super-Yang-Mills theory by making an exactly marginal deformation. The superconformal symmetry of the parent N=4 super-Yang-Mills theory is characterized by the Lie superalgebra psu(2,2|4), which seems to be broken to u(2,2|2) in the N=2 quiver gauge theory. We will show that the broken generators can be upgraded to quantum generators. As a result, the N=2 quiver gauge theory in fact has the full N=4 superconformal symmetry, albeit in a quantum deformed way.
We study four-dimensional Chern-Simons theory on D×C (where D is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model. This boundary theory gives rise to a current algebra that turns out to be an "analytically-continued" toroidal Lie algebra. In addition, we show how certain bulk correlation functions of two and three Wilson lines can be captured by boundary correlation functions of local operators in the three-dimensional WZW model. In particular, we reproduce the leading and subleading nontrivial contributions to the rational R-matrix purely from the boundary theory. Based on JHEP 02 (2021) 227.
Carlos Bercini, "The Wilson Loop - Large Spin OPE dictionary"
We work out the map between null polygonal hexagonal Wilson loops and spinning three point functions in large N conformal gauge theories by mapping the variables describing the two different physical quantities and by working out the precise normalization factors entering this duality. By fixing all the kinematics we open the ground for a precise study of the dynamics underlying these dualities – most notably through integrability in the case of planar maximally supersymmetric Yang-Mills theory.
Based on: arXiv:2110.04364 with Vasco Gonçalves, Alexandre Homrich, Pedro Vieira.
Aleix Gimenez-Grau, "Bootstrapping holographic defect correlators"
We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in N=4 SYM. We use inversion formula technology in order to reconstruct the CFT data starting from a single discontinuity of the correlator. In the planar strong coupling limit only a finite number of conformal blocks contributes to the discontinuity, which allows us to obtain elegant closed-form expressions for two-point functions of single-trace operators of weight J=2,3,4 . Our final result passes a number of non-trivial consistency checks: it has the correct discontinuity, it satisfies the superconformal Ward identities, it has a sensible expansion in both defect and bulk OPEs, and is consistent with available results coming from localization. The method is completely algorithmic and can be implemented to calculate correlators of arbitrary weight.
Himanshu Khanchandani, "CFT in AdS and Gross-Neveu BCFT"
I will start by describing how studying a CFT in AdS can give us non-trivial information about the corresponding BCFT on half space. Then I will use this idea to study Gross-Neveu BCFT. I will discuss various boundary phases for the large N Gross-Neveu model and show what they correspond to in an epsilon expansion description in d = 2 + epsilon and 4 - epsilon dimensions. Based on https://arxiv.org/abs/2110.04268.
Levente Pristyák, "Current operators in the XYZ model"
In recent years, Generalized Hydrodynamics (GHD) was developed to describe the Euler-scale transport properties of integrable systems. However, GHD so far was applied only to models with a global U(1) symmetry, leading to particle conservation. But the current operators, that describe the flow of the conserved charges can be defined even in the absence of particle conservation, and therefore can serve as the basis of a GHD setup. A well-known example of a model lacking U(1) symmetry is the XYZ spin chain. In my talk I present an ongoing investigation of the current operators and their mean values in this model, using a generalized Algebraic Bethe Ansatz.
Xinyu Zhang, "Hidden symmetry in 4d N=2 quiver gauge theory"
We study the global symmetry of 4d N=2 superconformal quiver gauge theory, which can be obtained from the orbifold projection of the N=4 super-Yang-Mills theory by making an exactly marginal deformation. The superconformal symmetry of the parent N=4 super-Yang-Mills theory is characterized by the Lie superalgebra psu(2,2|4), which seems to be broken to u(2,2|2) in the N=2 quiver gauge theory. We will show that the broken generators can be upgraded to quantum generators. As a result, the N=2 quiver gauge theory in fact has the full N=4 superconformal symmetry, albeit in a quantum deformed way.
Titles and abstracts for the fourth Gong Show
Ilija Buric, "Defect conformal blocks from the Iwasawa decomposition"
Defect conformal field theories are an important and interesting generalisation of ordinary CFTs. In recent years they received attention within the conformal bootstrap programme. I will report on a new realisation of correlation functions in a defect CFT obtained by group theoretic methods and based in particular on the Iwasawa decomposition of the defect conformal group. As the first application, I will show how this realisation is used to compute previously unknown conformal blocks for three-point correlation functions and express them in terms of Appell's functions. The talk is based on joint work with Volker Schomerus, [2012.12489].
Daniele Gregori, "Integrability and cycles of deformed N=2 gauge theory"
In this talk, I will briefly outline an example of a new kind of correspondence between integrable models and N=2 SYM theories, discovered through the use of the ODE/IM correspondence in its extended version with two singular irregular points. I will focus on the simplest example of the correspondence between pure N=2 SU(2) SYM in the Nekrasov-Shatashvili limit (deformed Seiberg-Witten (SW)) and the Liouville self-dual model, but we have shown that the correspondence holds more generally with some theories with massive flavours and higher rank gauge group. The main result of our correspondence is an identification between the Q, Y and T functions of integrability with the (deformed SW-) periods and masses of the gauge theories, from which also new results on both sides follow. Based on arXiv:1908.08030 with D. Fioravanti and also on work in progress with H. Shu.
Luigi Guerrini, "A duality for the latitude Wilson loop in ABJM"
I will discuss the operator dual to the latitude BPS Wilson loops in the ABJM model at k=1, and identify it as a novel bound state of Wilson and vortex loops by combining symmetry considerations and exact results from supersymmetric localization. An explicit description of the mixed operators as a supersymmetric quantum mechanics coupled to the bulk theory will also be provided.
Enrico Olivucci, "Hexagons in Fishnet theories: direct derivation"
I will discuss how to derive hexagon form factors in the Fishnet conformal field theory and its generalizations with fermions, starting from the Feynman diagrams. The technique is based on the integrability of a quantum conformal chain which naturally appears when cutting the diagrams between two external points.
Defect conformal field theories are an important and interesting generalisation of ordinary CFTs. In recent years they received attention within the conformal bootstrap programme. I will report on a new realisation of correlation functions in a defect CFT obtained by group theoretic methods and based in particular on the Iwasawa decomposition of the defect conformal group. As the first application, I will show how this realisation is used to compute previously unknown conformal blocks for three-point correlation functions and express them in terms of Appell's functions. The talk is based on joint work with Volker Schomerus, [2012.12489].
Daniele Gregori, "Integrability and cycles of deformed N=2 gauge theory"
In this talk, I will briefly outline an example of a new kind of correspondence between integrable models and N=2 SYM theories, discovered through the use of the ODE/IM correspondence in its extended version with two singular irregular points. I will focus on the simplest example of the correspondence between pure N=2 SU(2) SYM in the Nekrasov-Shatashvili limit (deformed Seiberg-Witten (SW)) and the Liouville self-dual model, but we have shown that the correspondence holds more generally with some theories with massive flavours and higher rank gauge group. The main result of our correspondence is an identification between the Q, Y and T functions of integrability with the (deformed SW-) periods and masses of the gauge theories, from which also new results on both sides follow. Based on arXiv:1908.08030 with D. Fioravanti and also on work in progress with H. Shu.
Luigi Guerrini, "A duality for the latitude Wilson loop in ABJM"
I will discuss the operator dual to the latitude BPS Wilson loops in the ABJM model at k=1, and identify it as a novel bound state of Wilson and vortex loops by combining symmetry considerations and exact results from supersymmetric localization. An explicit description of the mixed operators as a supersymmetric quantum mechanics coupled to the bulk theory will also be provided.
Enrico Olivucci, "Hexagons in Fishnet theories: direct derivation"
I will discuss how to derive hexagon form factors in the Fishnet conformal field theory and its generalizations with fermions, starting from the Feynman diagrams. The technique is based on the integrability of a quantum conformal chain which naturally appears when cutting the diagrams between two external points.
Titles and abstracts for the third Gong Show
Gabriel Bliard, "Mellin amplitudes for 1D CFT"
In this talk, I will present the construction of a Mellin transform which is tailored to 1d CFTs while preserving some of the key properties of its higher dimensional relative. Using the Regge boundedness and the OPE, I will sketch out the derivation of an infinite set of non-perturbative sum rules which can be tested with perturbative data. Finally, I will consider perturbations generated by quartic scalar interactions in AdS2 with L derivatives and present a recursive relation for the first order CFT data of these theories for any number of derivatives (4 L), as well as its explicit solution for L ranging from zero to six matching and extending the bootstrap-based results.
In this talk, I will present the construction of a Mellin transform which is tailored to 1d CFTs while preserving some of the key properties of its higher dimensional relative. Using the Regge boundedness and the OPE, I will sketch out the derivation of an infinite set of non-perturbative sum rules which can be tested with perturbative data. Finally, I will consider perturbations generated by quartic scalar interactions in AdS2 with L derivatives and present a recursive relation for the first order CFT data of these theories for any number of derivatives (4 L), as well as its explicit solution for L ranging from zero to six matching and extending the bootstrap-based results.
Fabrizio Del Monte, "BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations"
Five-dimensional SCFTs arise from the low-energy dynamics of M-theory compactified on local (toric) Calabi-Yau threefolds. Even though it often happens that such theories have a low-energy gauge theory phase, because the gauge coupling in five dimensions is an irrelevant parameter these SCFTs are intrinsically nonlagrangian. In this talk I will show how to extract detailed information about their BPS sector from the geometry of the toric Calabi-Yau, by the introduction of an associated graph, called a quiver. The quiver defines a discrete integrable system, whose solution determines the string coupling constant corrections to the Seiberg-Witten theory of the low-energy five-dimensional gauge theory: this gives both q-difference equations satisfied by the partition function of the five-dimensional theory compactified on a circle with finite radius, and its BPS spectrum in an appropriate chamber of the moduli space.
Five-dimensional SCFTs arise from the low-energy dynamics of M-theory compactified on local (toric) Calabi-Yau threefolds. Even though it often happens that such theories have a low-energy gauge theory phase, because the gauge coupling in five dimensions is an irrelevant parameter these SCFTs are intrinsically nonlagrangian. In this talk I will show how to extract detailed information about their BPS sector from the geometry of the toric Calabi-Yau, by the introduction of an associated graph, called a quiver. The quiver defines a discrete integrable system, whose solution determines the string coupling constant corrections to the Seiberg-Witten theory of the low-energy five-dimensional gauge theory: this gives both q-difference equations satisfied by the partition function of the five-dimensional theory compactified on a circle with finite radius, and its BPS spectrum in an appropriate chamber of the moduli space.
Nat Levine, "Embedding integrable sigma models in string theory"
Starting from integrable sigma-models, we will promote their coupling constants to functions of the 2d co-ordinates, e.g. time, and ask whether the resulting time-dependent model is still classically integrable (admits a flat Lax connection). The result, in a large set of examples, is that it is integrable if the time dependence matches the 1-loop RG flow, with 2d time interpreted as RG time. This is a surprising, new link between integrability and the RG flow. Such sigma-models with time-dependent couplings governed by the RG flow arise naturally in string theory in the light-cone gauge, suggesting the possibility of a large, new class of solvable string backgrounds. Based on 2008.01112.
Starting from integrable sigma-models, we will promote their coupling constants to functions of the 2d co-ordinates, e.g. time, and ask whether the resulting time-dependent model is still classically integrable (admits a flat Lax connection). The result, in a large set of examples, is that it is integrable if the time dependence matches the 1-loop RG flow, with 2d time interpreted as RG time. This is a surprising, new link between integrability and the RG flow. Such sigma-models with time-dependent couplings governed by the RG flow arise naturally in string theory in the light-cone gauge, suggesting the possibility of a large, new class of solvable string backgrounds. Based on 2008.01112.
Juan Miguel Nieto Garcia, "Three-parameter deformation of R×S3 in the Landau-Lifshitz limit"
I will present the effective field theory associated to the R×S3 sector of the three-parameter deformation of AdS3×S3×T4 in the Landau-Lifshitz approximation. I will show how to use this action to compute the dispersion relation of excitations around the BMN vacuum and the perturbative S-matrix associated to them. We are able to compute and sum all the different loop contributions to the S-matrix in this limit.
I will present the effective field theory associated to the R×S3 sector of the three-parameter deformation of AdS3×S3×T4 in the Landau-Lifshitz approximation. I will show how to use this action to compute the dispersion relation of excitations around the BMN vacuum and the perturbative S-matrix associated to them. We are able to compute and sum all the different loop contributions to the S-matrix in this limit.
Tomas Reis, "Renormalons from Resurgence"
Renormalons are a common but poorly understood feature of non-perturbative quantum field theory. Thanks to both resurgence and integrability, we can identify them and study them in toy models. While a general theory remains elusive, we find some insights, like how in some condensed matter systems renormalons are related to superconductivity.
Renormalons are a common but poorly understood feature of non-perturbative quantum field theory. Thanks to both resurgence and integrability, we can identify them and study them in toy models. While a general theory remains elusive, we find some insights, like how in some condensed matter systems renormalons are related to superconductivity.
Leonardo Santilli, "TTbar deformation of q-Yang-Mills theory"
I will present the TTbar-perturbed version of q-deformed two-dimensional Yang-Mills theory. The TTbar-operator spoils the factorization into chiral/anti-chiral sectors. On the other hand, it preserves a large N third order phase transition, although modifying the phase diagram. Implications for the entanglement entropy will be commented as well. I will conclude with comments on the potential applications of these results to integrability and to four-dimensional supersymmetric Yang-Mills theory. Based on joint work with Richard J. Szabo and Miguel Tierz, JHEP (2020) [arXiv:2009.00657].
I will present the TTbar-perturbed version of q-deformed two-dimensional Yang-Mills theory. The TTbar-operator spoils the factorization into chiral/anti-chiral sectors. On the other hand, it preserves a large N third order phase transition, although modifying the phase diagram. Implications for the entanglement entropy will be commented as well. I will conclude with comments on the potential applications of these results to integrability and to four-dimensional supersymmetric Yang-Mills theory. Based on joint work with Richard J. Szabo and Miguel Tierz, JHEP (2020) [arXiv:2009.00657].
Titles and abstracts for the second Gong Show
Sara Bonansea “Wilson loops correlators in defect N=4 SYM”
In this gong-show, I will present a work where we consider the correlator of two concentric circular Wilson loops with equal radii at strong coupling for arbitrary spatial and internal separation within a defect version of N=4 Super Yang-Mills theory, which is dual to the D3-D5 probe-brane system. Compared to the standard Gross-Ooguri transition between connected and disconnected minimal surfaces, a more involved pattern of saddle points contributes to the two-circles correlator due to the defect's presence. We analyse the transitions between different kinds of minimal surfaces and their dependence on the setting's numerous parameters.
Andrea Fontanella "Lie Algebra Expansion in Coset Sigma Models and Non-Relativistic String Theory"
Lie algebra expansion is a technique that allows to generate a new algebra, usually bigger, from a given one. I will sketch the idea of applying this technique to coset sigma models with Z4 automorphism in order to generate new sigma models. The main result is that this family of new models admit a Lax pair if a certain set of conditions on the truncation of the Lie algebra is imposed. I will briefly discuss the connection of Lie algebra expansion to non-relativistic string theory, and I will mention ongoing projects in this latter topic. This is based on arXiv:2005.01736 with L. Romano and on work in progress with J.M. Nieto, A. Torrielli and S. van Tongeren.
Suvajit Majumder "Protected states in AdS3xS3xT4 from integrability"
I will briefly review algebraic Bethe ansatz(ABA) in the context of AdS3/CFT2. Specialising the discussion to massless modes in AdS3xS3xT4, I will introduce an R-matrix in relativistic variables and use the zero-momentum limit of the ABA to compute the protected spectrum in this background. I will extend the construction to K3 background (realised as orbifolds of T4).
Gerben Oling "Non-relativistic strings and limits of AdS/CFT"
We construct novel backgrounds for non-relativistic strings, which are dual to the decoupling limits of N=4 SYM that lead to Spin Matrix theories (SMTs). On the boundary, these SMTs are obtained by zooming in on particular BPS bounds and the resulting theory is non-relativistic. Likewise, the bulk dual of the SMT limit gives a covariant non-relativistic string theory. The resulting bulk backgrounds lead to novel sigma models and also reproduce known ones. We point out how a natural symplectic structure arises in the SMT limit, which explains the field redefinitions that were used by Klose and Zarembo to compute the exact S-matrix of the Landau-Lifshitz sigma model and possibly generalizes them to the novel sigma models.
Chiara Paletta "Integrable open quantum systems"
The evolution of the density matrix of an open quantum system is generated by a Liouvillian superoperator dependent on the Hamiltonian H of the system and a Lindblad operator A describing the coupling to the environment. In this gong-show, I will present how to construct this superoperator for spin chains. Then, by using the boost automorphism, I will show how to construct integrable superoperators from H and A of different type (e.g. 6-vertex type). These models excitingly describe
exactly solvable open quantum system.
Davide Polvara "From tree-level perturbation theory to the S-matrix bootstrap in two dimensions"
In the past the bootstrap program has been used to find analytical results for the S-matrix of a variety of (1+1)-dimensional integrable models. Its connection to standard Feynman diagram computations is however still unclear, as is the underlying mechanism responsible for the cancellation of all non-elastic processes. In this talk I will show how bootstrap relations connecting different S-matrix elements and the absence of non-elastic scattering emerge at tree-level from perturbation theory for the class of untwisted affine Toda theories.
Anton Pribytok "Deformed AdS integrability and Free Fermion condition"
We study regular solution space of YBE, where the sector is spanned by spin chains up to 8 vertices with nearest-neighbour interaction. In this framework one finds four solutions, two of which are associated to 6- and 8-vertex models with R-matrices of difference form dependence, whereas overall approach accounts for arbitrary spectral dependence to investigate AdS integrable models and generalisations. The other two appear to be novel one-parameter deformed models that allow embeddings and admit AdS_{2,3} S-matrices as special cases. In addition, we address generalised integrable models with 2-, 3- and 4-dimensional local space (including 15-vertex and Zhiber-Shabat-Mikhailov deformation and field-theoretic description of such class). In the latter case, we look for AdS_5 deformations (generalised Hubbard model) by different methods, which take into account generalisation of U_q(psu(2,2|4)) and address relation to Korepanov generic construction of scattering matrix for Zamolodchikov algebra, such construction also possesses reduction point to AdS_5 as a special case (bi-layer construction of Mitev-Staudacher-Tsuboi and Shiroishi-Wadati are currently under investigation). For the aforementioned AdS models we also demonstrate free-fermion condition emergence and we prove that it is satisfied for novel AdS_{2,3} models, further direction includes FF derivation for generalised AdS_5 sector from above. In addition, extended deformations of sl(2) sector and resolution of flux implementation cover ongoing research and relevant discussion provided (extension of Kulish model, associated Belavin-Drinfeld algebras and Yangians).
Based on arXiv: 2003.04332, 2010.11231, 2011.08217, 2012.xxxxx (AdS integrability and deformed algebras)
In this gong-show, I will present a work where we consider the correlator of two concentric circular Wilson loops with equal radii at strong coupling for arbitrary spatial and internal separation within a defect version of N=4 Super Yang-Mills theory, which is dual to the D3-D5 probe-brane system. Compared to the standard Gross-Ooguri transition between connected and disconnected minimal surfaces, a more involved pattern of saddle points contributes to the two-circles correlator due to the defect's presence. We analyse the transitions between different kinds of minimal surfaces and their dependence on the setting's numerous parameters.
Andrea Fontanella "Lie Algebra Expansion in Coset Sigma Models and Non-Relativistic String Theory"
Lie algebra expansion is a technique that allows to generate a new algebra, usually bigger, from a given one. I will sketch the idea of applying this technique to coset sigma models with Z4 automorphism in order to generate new sigma models. The main result is that this family of new models admit a Lax pair if a certain set of conditions on the truncation of the Lie algebra is imposed. I will briefly discuss the connection of Lie algebra expansion to non-relativistic string theory, and I will mention ongoing projects in this latter topic. This is based on arXiv:2005.01736 with L. Romano and on work in progress with J.M. Nieto, A. Torrielli and S. van Tongeren.
Suvajit Majumder "Protected states in AdS3xS3xT4 from integrability"
I will briefly review algebraic Bethe ansatz(ABA) in the context of AdS3/CFT2. Specialising the discussion to massless modes in AdS3xS3xT4, I will introduce an R-matrix in relativistic variables and use the zero-momentum limit of the ABA to compute the protected spectrum in this background. I will extend the construction to K3 background (realised as orbifolds of T4).
Gerben Oling "Non-relativistic strings and limits of AdS/CFT"
We construct novel backgrounds for non-relativistic strings, which are dual to the decoupling limits of N=4 SYM that lead to Spin Matrix theories (SMTs). On the boundary, these SMTs are obtained by zooming in on particular BPS bounds and the resulting theory is non-relativistic. Likewise, the bulk dual of the SMT limit gives a covariant non-relativistic string theory. The resulting bulk backgrounds lead to novel sigma models and also reproduce known ones. We point out how a natural symplectic structure arises in the SMT limit, which explains the field redefinitions that were used by Klose and Zarembo to compute the exact S-matrix of the Landau-Lifshitz sigma model and possibly generalizes them to the novel sigma models.
Chiara Paletta "Integrable open quantum systems"
The evolution of the density matrix of an open quantum system is generated by a Liouvillian superoperator dependent on the Hamiltonian H of the system and a Lindblad operator A describing the coupling to the environment. In this gong-show, I will present how to construct this superoperator for spin chains. Then, by using the boost automorphism, I will show how to construct integrable superoperators from H and A of different type (e.g. 6-vertex type). These models excitingly describe
exactly solvable open quantum system.
Davide Polvara "From tree-level perturbation theory to the S-matrix bootstrap in two dimensions"
In the past the bootstrap program has been used to find analytical results for the S-matrix of a variety of (1+1)-dimensional integrable models. Its connection to standard Feynman diagram computations is however still unclear, as is the underlying mechanism responsible for the cancellation of all non-elastic processes. In this talk I will show how bootstrap relations connecting different S-matrix elements and the absence of non-elastic scattering emerge at tree-level from perturbation theory for the class of untwisted affine Toda theories.
Anton Pribytok "Deformed AdS integrability and Free Fermion condition"
We study regular solution space of YBE, where the sector is spanned by spin chains up to 8 vertices with nearest-neighbour interaction. In this framework one finds four solutions, two of which are associated to 6- and 8-vertex models with R-matrices of difference form dependence, whereas overall approach accounts for arbitrary spectral dependence to investigate AdS integrable models and generalisations. The other two appear to be novel one-parameter deformed models that allow embeddings and admit AdS_{2,3} S-matrices as special cases. In addition, we address generalised integrable models with 2-, 3- and 4-dimensional local space (including 15-vertex and Zhiber-Shabat-Mikhailov deformation and field-theoretic description of such class). In the latter case, we look for AdS_5 deformations (generalised Hubbard model) by different methods, which take into account generalisation of U_q(psu(2,2|4)) and address relation to Korepanov generic construction of scattering matrix for Zamolodchikov algebra, such construction also possesses reduction point to AdS_5 as a special case (bi-layer construction of Mitev-Staudacher-Tsuboi and Shiroishi-Wadati are currently under investigation). For the aforementioned AdS models we also demonstrate free-fermion condition emergence and we prove that it is satisfied for novel AdS_{2,3} models, further direction includes FF derivation for generalised AdS_5 sector from above. In addition, extended deformations of sl(2) sector and resolution of flux implementation cover ongoing research and relevant discussion provided (extension of Kulish model, associated Belavin-Drinfeld algebras and Yangians).
Based on arXiv: 2003.04332, 2010.11231, 2011.08217, 2012.xxxxx (AdS integrability and deformed algebras)
Titles and abstracts for the first Gong Show
Stefano Baiguera "Non-relativistic near-BPS corners of N=4 super Yang-Mills with SU(1,1) symmetry"
Spin Matrix Theories (SMT) are non-relativistic quantum mechanical models arising from particular decoupling limits of N=4 super Yang-Mills (SYM) near a BPS bound. In this talk we focus on sectors for which a SU(1,1) structure is preserved and we show that they can be obtained at the classical level by reduction of N=4 SYM on a three-sphere. Upon quantization, and taking into account normal ordering, they match the corresponding limits of the one-loop dilatation operator, thus establishing the consistency of the procedure at the quantum level. In the particular case of SU(1,1|1) SMT, we find a tantalizing superfield formulation which includes the full interaction. All the cases have a semi-local formulation as (1+1)-dimensional non-relativistic quantum field theories living on a circle.
Ilija Buric "From Integrable Gaudin Models to Multipoint Conformal Blocks"
The study of crossing symmetry for higher-point correlation functions is a promising new direction within d-dimensional conformal bootstrap. I will report on a recently discovered characterisation of the relevant multipoint conformal blocks as eigenfunctions of a set of Gaudin Hamiltonians. This observation opens the way to study these partial waves using methods of integrability. The talk is based on the joint work with S. Lacroix, J. A. Mann, L. Quintavalle and V. Schomerus, [2009.11882].
Julius Julius "Baxter Equation for Boundary Integrability"
I will describe the Baxter equation whose solutions contain the non-perturbative spectrum of certain boundary integrable systems related to Maldacena-Wilson loops in N=4 supersymmetric Yang-Mills theory.
The first system that I will consider is the cusped Maldacena-Wilson line in the so-called ladders limit, with orthogonal scalar insertions at the cusp. Here we will see that this setup can be described by a dual open fishchain - a discretised open string. I will show that this system is integrable at the quantum level and derive the Baxter equation to obtain the non-perturbative spectrum of an arbitrary number of L orthogonal insertions.
The spectrum of the Baxter equation contains excited states which can be shown to correspond to parallel insertions --- i.e. scalars spanned by those that couple to the line. The J^th excited state corresponds to an insertion of J parallel scalars. For the case of L = 0, i.e. the case with no orthogonal insertions, one can go away from the ladders limit, and take the straight line limit of the Wilson line to obtain the one-dimensional defect CFT that lives on the 1/2-BPS infinite straight Maldacena-Wilson line - the second system that I consider. The excited states of the Baxter equation can be mapped to states in the defect CFT. Starting with the Quantum Spectral Curve (QSC) for these excited states, I will derive the Baxter equation that captures the spectrum of an arbitrary number of J parallel insertions. I will also display some analytical results at weak and strong coupling, and show that the numerical solution obtained from the QSC interpolates between them at finite coupling.
Rob Klabbers "How coordinate Bethe ansatz works for Inozemtsev model"
I would like to report on recent progress (https://arxiv.org/abs/2009.14513) on Inozemtsev's elliptic spin chain, an isotropic spin chain with elliptic pair potential that interpolates between the Heisenberg XXX spin chain and the long-range Haldane-Shastry spin chain that has been of interest to the integrability community for some time. Progress was made on understanding the 'extended coordinate Bethe ansatz' used to solve the eigenvalue problem, by identifying better coordinates such as quasimomenta. In the new coordinates, the energy becomes close to additive. Moreover, in these coordinates both the Bethe-ansatz equations and the energy become elliptic functions, allowing for a lifting of the spectral problem to the elliptic curve, effectively rationalising it as one might expect for an isotropic spin chain. Finally, I will show how the Inozemtsev model links the scattering states of the Heisenberg model to the Yangian highest-weight states of Haldane Shastry, while Heisenberg bound states become affine descendants in the Haldane-Shastry spectrum.
Yuan Miao "On the Q-operator and the spectrum of the XXZ model at root of unity"
For quantum XXZ spin chain (6-vertex model), We propose a construction of Baxter’s Q-operator at any anisotropy from a new type of two-parameter transfer matrix. This transfer matris can be decomposed in a way that provides an alternative proof for the transfer matrix fusion and Wronskian relations. At root of unity a special decomposition further allows us to construct the Q-operator explicitly, and from it we prove a conjecture of De Luca et al. We elucidate the exact n-strings (Fabricius–McCoy strings) and the exponential degeneracies in the spectrum of the (usual) transfer matrix at root of unity after deriving truncated fusion and Wronskian relation, complementing the existing ones. We connect our findings with the ‘string-charge duality’ in the thermodynamic limit, leading toward potential applications, e.g. in the regime of out-of-equilibrium physics for quantum integrable systems.
Anne Spiering "Integrability and Quantum Chaos in N=4 SYM from the Spectral Rigidity"
The discovery of integrability in planar N=4 SYM theory led to considerable advances in the computation of the planar anomalous dimension spectrum. Less is known at the non-planar level where the theory is assumed to be non-integrable. Focussing on the spectral rigidity, I will show how statistical properties of numerical anomalous dimension spectra can give insight into the symmetries of the underlying model and that the non-planar spectrum is well described by random matrix theory. This talk complements Tristan’s LIJC talk.
Spin Matrix Theories (SMT) are non-relativistic quantum mechanical models arising from particular decoupling limits of N=4 super Yang-Mills (SYM) near a BPS bound. In this talk we focus on sectors for which a SU(1,1) structure is preserved and we show that they can be obtained at the classical level by reduction of N=4 SYM on a three-sphere. Upon quantization, and taking into account normal ordering, they match the corresponding limits of the one-loop dilatation operator, thus establishing the consistency of the procedure at the quantum level. In the particular case of SU(1,1|1) SMT, we find a tantalizing superfield formulation which includes the full interaction. All the cases have a semi-local formulation as (1+1)-dimensional non-relativistic quantum field theories living on a circle.
Ilija Buric "From Integrable Gaudin Models to Multipoint Conformal Blocks"
The study of crossing symmetry for higher-point correlation functions is a promising new direction within d-dimensional conformal bootstrap. I will report on a recently discovered characterisation of the relevant multipoint conformal blocks as eigenfunctions of a set of Gaudin Hamiltonians. This observation opens the way to study these partial waves using methods of integrability. The talk is based on the joint work with S. Lacroix, J. A. Mann, L. Quintavalle and V. Schomerus, [2009.11882].
Julius Julius "Baxter Equation for Boundary Integrability"
I will describe the Baxter equation whose solutions contain the non-perturbative spectrum of certain boundary integrable systems related to Maldacena-Wilson loops in N=4 supersymmetric Yang-Mills theory.
The first system that I will consider is the cusped Maldacena-Wilson line in the so-called ladders limit, with orthogonal scalar insertions at the cusp. Here we will see that this setup can be described by a dual open fishchain - a discretised open string. I will show that this system is integrable at the quantum level and derive the Baxter equation to obtain the non-perturbative spectrum of an arbitrary number of L orthogonal insertions.
The spectrum of the Baxter equation contains excited states which can be shown to correspond to parallel insertions --- i.e. scalars spanned by those that couple to the line. The J^th excited state corresponds to an insertion of J parallel scalars. For the case of L = 0, i.e. the case with no orthogonal insertions, one can go away from the ladders limit, and take the straight line limit of the Wilson line to obtain the one-dimensional defect CFT that lives on the 1/2-BPS infinite straight Maldacena-Wilson line - the second system that I consider. The excited states of the Baxter equation can be mapped to states in the defect CFT. Starting with the Quantum Spectral Curve (QSC) for these excited states, I will derive the Baxter equation that captures the spectrum of an arbitrary number of J parallel insertions. I will also display some analytical results at weak and strong coupling, and show that the numerical solution obtained from the QSC interpolates between them at finite coupling.
Rob Klabbers "How coordinate Bethe ansatz works for Inozemtsev model"
I would like to report on recent progress (https://arxiv.org/abs/2009.14513) on Inozemtsev's elliptic spin chain, an isotropic spin chain with elliptic pair potential that interpolates between the Heisenberg XXX spin chain and the long-range Haldane-Shastry spin chain that has been of interest to the integrability community for some time. Progress was made on understanding the 'extended coordinate Bethe ansatz' used to solve the eigenvalue problem, by identifying better coordinates such as quasimomenta. In the new coordinates, the energy becomes close to additive. Moreover, in these coordinates both the Bethe-ansatz equations and the energy become elliptic functions, allowing for a lifting of the spectral problem to the elliptic curve, effectively rationalising it as one might expect for an isotropic spin chain. Finally, I will show how the Inozemtsev model links the scattering states of the Heisenberg model to the Yangian highest-weight states of Haldane Shastry, while Heisenberg bound states become affine descendants in the Haldane-Shastry spectrum.
Yuan Miao "On the Q-operator and the spectrum of the XXZ model at root of unity"
For quantum XXZ spin chain (6-vertex model), We propose a construction of Baxter’s Q-operator at any anisotropy from a new type of two-parameter transfer matrix. This transfer matris can be decomposed in a way that provides an alternative proof for the transfer matrix fusion and Wronskian relations. At root of unity a special decomposition further allows us to construct the Q-operator explicitly, and from it we prove a conjecture of De Luca et al. We elucidate the exact n-strings (Fabricius–McCoy strings) and the exponential degeneracies in the spectrum of the (usual) transfer matrix at root of unity after deriving truncated fusion and Wronskian relation, complementing the existing ones. We connect our findings with the ‘string-charge duality’ in the thermodynamic limit, leading toward potential applications, e.g. in the regime of out-of-equilibrium physics for quantum integrable systems.
Anne Spiering "Integrability and Quantum Chaos in N=4 SYM from the Spectral Rigidity"
The discovery of integrability in planar N=4 SYM theory led to considerable advances in the computation of the planar anomalous dimension spectrum. Less is known at the non-planar level where the theory is assumed to be non-integrable. Focussing on the spectral rigidity, I will show how statistical properties of numerical anomalous dimension spectra can give insight into the symmetries of the underlying model and that the non-planar spectrum is well described by random matrix theory. This talk complements Tristan’s LIJC talk.