Exact S-matrices for supersymmetric sigma models and the Potts model

TL;DR

This paper develops algebraic formulations of exact S-matrices for supersymmetric sigma models and the Potts model, revealing their algebraic equivalences and applications to quantum Hall transitions and coupling flows.

Contribution

It constructs new S-matrices for supersymmetric sigma models using Temperley-Lieb algebra representations, unifying different formulations and exploring their physical implications.

Findings

Different Potts S-matrix formulations are algebraically equivalent.

Constructed S-matrices for sigma models with sl(m+n|n) supersymmetry.

Applied S-matrices to quantum Hall transition and coupling flow scenarios.

Abstract

We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at theta=pi by a small change in the topological angle theta. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma models.