Dualised sigma-models at the two-loop order

TL;DR

This paper investigates the quantum equivalence of non-abelian dual sigma-models at the two-loop level, demonstrating that the T-dualized SU(2) model remains renormalizable with finite modifications to the target space metric.

Contribution

It proves that the T-dualized SU(2) sigma-model is renormalizable at two loops, with divergences absorbed into finite redefinitions, confirming its quantum consistency.

Findings

The model is renormalizable at two-loop order.

Divergences are absorbed into finite redefinitions of couplings and fields.

Quantum equivalence with the original model is maintained at this order.

Abstract

We adress ourselves the question of the quantum equivalence of non abelian dualised $\si$-models on the simple example of the T-dualised $SU(2) \si$-model. This theory is classically canonically equivalent to the standard chiral $SU(2) \si$-model. It is known that the equivalence also holds at the first order in perturbations with the same $\be$ functions. However, this model has been claimed to be non-renormalisable at the two-loop order. The aim of the present work is the proof that it is - at least up to this order - still possible to define a correct quantum theory. Its target space metric being only modified in a finite manner, all divergences are reabsorbed into coupling and fields (infinite) renormalisations.