Dual description of $\eta$-deformed OSP sigma models

TL;DR

This paper explores the dual description of $ a$-deformed $OSP(N|2m)$ sigma models, revealing their connection to Toda quantum field theories and matching their scattering matrices with trigonometric $S$-matrices.

Contribution

It introduces a continuous parameter-dependent screening charge system for $ a$-deformed supergroup sigma models and establishes their relation to Toda QFTs and known scattering matrices.

Findings

Leading UV asymptotics match a perturbed Gaussian theory.

Tree-level scattering matrix aligns with trigonometric $OSP(N|2m)$ $S$-matrix expansion.

Proposes a novel dual description involving Toda quantum field theories.

Abstract

We study the dual description of the $\eta$-deformed $OSP(N|2m)$ sigma model in the asymptotically free regime ($N>2m+2$). Compared to the case of classical Lie groups, for supergroups there are inequivalent $\eta$-deformations corresponding to different choices of simple roots. For a class of such deformations we propose the system of screening charges depending on a continuous parameter $b$, which defines the $\eta$-deformed $OSP(N|2m)$ sigma model in the limit $b\rightarrow\infty$ and a certain Toda QFT as $b\rightarrow0$. In the sigma model regime we show that the leading UV asymptotic of the $\eta$-deformed model coincides with a perturbed Gaussian theory. In the perturbative regime $b\rightarrow0$ we show that the tree-level two-particle scattering matrix matches the expansion of the trigonometric $OSP(N|2m)$ $S$-matrix.