Quantum equivalence of sigma models related by non Abelian Duality Transformations

TL;DR

This paper investigates the quantum equivalence of sigma models related by non-Abelian duality, showing that their coupling constant renormalization behavior is consistent at one loop and examining the breaking of equivalence at two loops.

Contribution

It demonstrates quantum equivalence of dual sigma models at one loop and explores the breakdown of this equivalence at two loops in specific models.

Findings

Dual models share the same one-loop renormalization behavior.

Two-loop equivalence is broken in the O(3) sigma model.

The models interpolate between SU(2) principal and O(3) sigma models.

Abstract

Coupling constant renormalization is investigated in 2 dimensional sigma models related by non Abelian duality transformations. In this respect it is shown that in the one loop order of perturbation theory the duals of a one parameter family of models, interpolating between the SU(2) principal model and the O(3) sigma model, exhibit the same behaviour as the original models. For the O(3) model also the two loop equivalence is investigated, and is found to be broken just like in the already known example of the principal model.