Quantum corrections of Abelian Duality Transformations

TL;DR

This paper proposes a modified Abelian Duality transformation ensuring quantum equivalence of sigma-models up to two loops, involving a non-standard perturbative approach and explicit formulas for specific models.

Contribution

It introduces a novel modification to Abelian Duality transformations that guarantees quantum equivalence at two-loop order, with explicit formulas for certain sigma-models.

Findings

Modified duality transformation guarantees quantum equivalence up to two loops.

Explicit formulas provided for a class of block diagonal purely metric sigma-models.

Non-standard perturbative treatment of the dual sigma-model is developed.

Abstract

A modification of the Abelian Duality transformations is proposed guaranteeing that a (not necessarily conformally invariant) $\sigma$-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires a somewhat non standard perturbative treatment of the {\sl dual} $\sigma$-model. Explicit formulae of the modified duality transformation are presented for a special class of block diagonal purely metric $\sigma$-models.