Integrability of a family of quantum field theories related to sigma models

TL;DR

This paper introduces a method to construct lattice discretizations of integrable quantum field theories, exemplified through models related to sigma models, including supersymmetric and string theory-relevant cases.

Contribution

A novel two-step method for discretizing integrable quantum field theories using quantum algebraic structures and representation theory, applied to multiple models including supersymmetric and string-related theories.

Findings

Constructed lattice Lax matrices and R-matrices for models

Demonstrated the method on four integrable models

Connected models to sigma models and string theory reductions

Abstract

A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The Sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2|1) Toda theory, and the N=2 supersymmetric Sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric Sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS_2 x S^2, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space.