Perturbative Quantum (In)equivalence of Dual $\sigma$ Models in $2$ dimensions

TL;DR

This paper investigates the quantum equivalence of dual sigma models in two dimensions, revealing that naive duality transformations lead to inequivalence at two-loop order in perturbation theory.

Contribution

It demonstrates that naive duality rules do not preserve quantum equivalence at two loops, highlighting the need for refined duality transformations in quantum sigma models.

Findings

Naive duality transformations fail to maintain equivalence at two loops.

Both Abelian and non-Abelian dual models are affected.

Quantum corrections break classical duality relations.

Abstract

Various examples of target space duality transformations are investigated up to two loop order in perturbation theory. Our results show that when using the tree level (`naive') transformation rules the dual theories are in general {\it inequivalent} at two loops to the original ones, (both for the Abelian and the non Abelian duality).