Staircase Models from Affine Toda Field Theory

TL;DR

This paper introduces a new class of elastic scattering theories based on affine Toda field theories, exploring their RG flow and connections to W_g minimal models.

Contribution

It generalizes the staircase model using affine Toda theories at complex couplings, providing analytic support for their RG flow behavior.

Findings

Supports the conjecture of RG flow visiting each W_g minimal model

Extends the staircase model to affine Toda field theories for A,D,E types

Provides analytic arguments for the flow structure

Abstract

We propose a class of purely elastic scattering theories generalising the staircase model of Al. B. Zamolodchikov, based on the affine Toda field theories for simply-laced Lie algebras g=A,D,E at suitable complex values of their coupling constants. Considering their Thermodynamic Bethe Ansatz equations, we give analytic arguments in support of a conjectured renormalisation group flow visiting the neighbourhood of each W_g minimal model in turn.