On quantum equivalence of dual sigma models: $SL(3)$ examples

TL;DR

This paper examines the quantum equivalence of certain $SL(3)$ sigma models and their Abelian duals at two-loop order, focusing on their $eta$ functions and the influence of discrete symmetries.

Contribution

It provides a detailed two-loop analysis of $SL(3)$ sigma models and their duals, highlighting conditions for quantum equivalence and the role of symmetries.

Findings

$SL(3)$ models and duals have matching $eta$ functions at two loops under certain conditions.

Discrete global symmetries significantly influence the quantum equivalence.

The study clarifies the conditions for quantum equivalence in non-Abelian sigma models.

Abstract

The equivalence of several $SL(3)$ sigma models and their special Abelian duals is investigated in the two loop order of perturbation theory. The investigation is based on extracting and comparing various $\beta$ functions of the original and dual models. The role of the discrete global symmetries is emphasized.