Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models

TL;DR

This paper develops the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models, providing evidence for the correct S matrix, exploring unconventional features, and revealing dualities with other models.

Contribution

It introduces the TBA for these models, supports the proposed GN S matrix, and uncovers a duality with SO(4) sigma and GN models, also critiquing a proposed S matrix for the flow into the random bond Ising model.

Findings

Confirmed the proposed GN S matrix by Bassi and Leclair

Discovered a relation between the sigma model and complex sine-Gordon model

Identified a duality between OSp(2|2) models and SO(4) models

Abstract

We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular a relation between this sigma model and the complex sine-Gordon model at a particular value of the coupling. We uncover an intriguing duality between the OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN model) on the other, somewhat generalizing to the massive case recent results on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into the random bond Ising model proposed by Cabra et al. [39], and conclude that their S matrix cannot be correct.