Solution of the Thirring Model with Imaginary Mass and Massless Scattering

TL;DR

This paper explicitly solves the Thirring model with imaginary mass using Bethe ansatz, revealing massless excitations with non-trivial scattering and confirming a conjectured S matrix result.

Contribution

It provides an explicit Bethe ansatz solution for the imaginary mass Thirring model and characterizes its massless scattering behavior.

Findings

Identification of left and right moving massless excitations

Computation of the S matrix confirming conjectures

Analysis of the model's relation to minimal conformal theories

Abstract

The Thirring model with imaginary mass (or the sine-Gordon model with imaginary coupling) is deeply related to all the flows between minimal conformal theories. We solve this model explicitely using the Bethe ansatz. We find that there are Left and Right moving massless excitations with non trivial LR scattering. We compute the S matrix and recover the result conjectured by Fendley et al.