Andrea Cavaglia
Title: Twisting Symmetries in large-N Quantum Field Theories
Abstract: I will introduce a new class of operators in a quantum field theory with a 't Hooft large N limit. They arise as a deformation of the standard local operators of the theory by parameters called twists. The twists allow us to break the symmetries of the original theory in a controllable way, including the space-time symmetries. I will explain why this construction is very useful in the context of integrable theories such as N=4 supersymmetric Yang-Mills theory. In this case, the twisting of the symmetries of the model may actually help us to solve it completely.
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Anastasia Doikou
Title: Set-theoretical Yang-Baxter and reflection equations and quantum group symmetries
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Valentina Forini
Title: AdS/CFT and string sigma-model, perturbatively and beyond
Abstract: “Solving" a four-dimensional gauge theory is a hard problem, which the AdS/CFT duality suggests to trade with “solving” a (highly non-trivial) two-dimensional theory for the string worldsheet.
I will discuss progress on perturbative and non-perturbative approaches to the study of string sigma-models relevant in AdS/CFT.
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Vidas Regelskis
Title: Algebraic Bethe ansatz for orthogonal and symplectic spin chains
The algebraic Bethe ansatz has been very fruitful in the study of gl(n)-symmetric integrable models. The study of the so(n)- and sp(n)-symmetric models so far has been less productive. One of the obstacles is that the R-matrix in this case is not quite of a six-vertex type, which is the key property used in the study of the gl(n)-symmetric models. Another obstacle is that not every irreducible highest weight so(n)- or sp(n)-representation can be lifted to a representation of the corresponding quantum group, such as Yangian or quantum loop algebra. The algebraic Bethe ansatz for so(n)- and sp(n)-symmetric periodic spin chains in the rational setting has been presented by De Vega and Karowski and Reshetikhin back in 80's. 30 years later I will explain how their ideas can be lifted to the trigonometric setting.
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Takanobu Taira
Title: Pseudo-Hermitian approach to Goldstone's theorem in non-Hermitian quantum field theory.
Abstract: We study the interplay between spontaneously breaking global/local continuous and discrete antilinear symmetries in a newly proposed general class of non-Hermitian quantum field theories containing complex scalar fields. We present a detailed analysis for non-Hermitian field theories with two/three complex scalar fields in the fundamental representation of SU(2) symmetry group. In the PT-symmetric regime and at the standard exceptional point the Goldstone theorem is shown to apply, although different identification procedures need to be employed. At the zero exceptional points, the Goldstone boson can not be identified. Comparing our approach, based on the pseudo-Hermiticity of the model, to an alternative approach that utilises surface terms to achieve compatibility for the non-Hermitian system, we find that the explicit forms of the Goldstone boson fields are different.
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Peter West
Title: E theory
Abstract: I will explain that the theory of strings and branes possess a very large Kac-Moody symmetry (E11). This theory has an infinite number of fields that live in a spacetime with an infinite number of coordinates. The symmetry determines the equations of motion of the low energy effective action and, if we restrict the fields and coordinates to be those we are familiar with, these equations are those of maximal supergravity. The physical meaning of the additional fields and coordinates will be discussed.
Title: Twisting Symmetries in large-N Quantum Field Theories
Abstract: I will introduce a new class of operators in a quantum field theory with a 't Hooft large N limit. They arise as a deformation of the standard local operators of the theory by parameters called twists. The twists allow us to break the symmetries of the original theory in a controllable way, including the space-time symmetries. I will explain why this construction is very useful in the context of integrable theories such as N=4 supersymmetric Yang-Mills theory. In this case, the twisting of the symmetries of the model may actually help us to solve it completely.
_______________________________________________________________________________________________________
Anastasia Doikou
Title: Set-theoretical Yang-Baxter and reflection equations and quantum group symmetries
________________________________________________________________________________________
Valentina Forini
Title: AdS/CFT and string sigma-model, perturbatively and beyond
Abstract: “Solving" a four-dimensional gauge theory is a hard problem, which the AdS/CFT duality suggests to trade with “solving” a (highly non-trivial) two-dimensional theory for the string worldsheet.
I will discuss progress on perturbative and non-perturbative approaches to the study of string sigma-models relevant in AdS/CFT.
_______________________________________________________________________________________________________
Vidas Regelskis
Title: Algebraic Bethe ansatz for orthogonal and symplectic spin chains
The algebraic Bethe ansatz has been very fruitful in the study of gl(n)-symmetric integrable models. The study of the so(n)- and sp(n)-symmetric models so far has been less productive. One of the obstacles is that the R-matrix in this case is not quite of a six-vertex type, which is the key property used in the study of the gl(n)-symmetric models. Another obstacle is that not every irreducible highest weight so(n)- or sp(n)-representation can be lifted to a representation of the corresponding quantum group, such as Yangian or quantum loop algebra. The algebraic Bethe ansatz for so(n)- and sp(n)-symmetric periodic spin chains in the rational setting has been presented by De Vega and Karowski and Reshetikhin back in 80's. 30 years later I will explain how their ideas can be lifted to the trigonometric setting.
______________________________________________________________________________________________________
Takanobu Taira
Title: Pseudo-Hermitian approach to Goldstone's theorem in non-Hermitian quantum field theory.
Abstract: We study the interplay between spontaneously breaking global/local continuous and discrete antilinear symmetries in a newly proposed general class of non-Hermitian quantum field theories containing complex scalar fields. We present a detailed analysis for non-Hermitian field theories with two/three complex scalar fields in the fundamental representation of SU(2) symmetry group. In the PT-symmetric regime and at the standard exceptional point the Goldstone theorem is shown to apply, although different identification procedures need to be employed. At the zero exceptional points, the Goldstone boson can not be identified. Comparing our approach, based on the pseudo-Hermiticity of the model, to an alternative approach that utilises surface terms to achieve compatibility for the non-Hermitian system, we find that the explicit forms of the Goldstone boson fields are different.
__________________________________________________________________________________________________
Peter West
Title: E theory
Abstract: I will explain that the theory of strings and branes possess a very large Kac-Moody symmetry (E11). This theory has an infinite number of fields that live in a spacetime with an infinite number of coordinates. The symmetry determines the equations of motion of the low energy effective action and, if we restrict the fields and coordinates to be those we are familiar with, these equations are those of maximal supergravity. The physical meaning of the additional fields and coordinates will be discussed.