Quantum correction to generalized T-dualities

TL;DR

This paper extends Poisson-Lie duality to include two-loop '-corrections in string theory, showing that the duality map requires modifications due to anomalous Lorentz transformations at higher orders.

Contribution

It demonstrates that Poisson-Lie duality can be extended to ' order with a corrected map accounting for Lorentz anomalies, advancing the understanding of dualities in string theory.

Findings

'-corrections modify the Poisson-Lie duality map.

Lorentz anomalies induce necessary corrections at two-loop order.

Duality remains valid with corrected '-dependent transformations.

Abstract

Poisson-Lie duality is a generalization of abelian and non-abelian T-duality, and it can be viewed as a map between solutions of the low-energy effective equations of string theory, i.e. at the (super)gravity level. We show that this fact extends to the next order in $\alpha'$ (two loops in $\sigma$-model perturbation theory) provided that the map is corrected. The $\alpha'$-correction to the map is induced by the anomalous Lorentz transformations of the fields that are necessary to go from a doubled $O(D,D)$-covariant formulation to the usual (super)gravity description.