On T-Duality and Integrability for Strings on AdS Backgrounds

TL;DR

This paper explores how T-duality affects integrability in string sigma models on AdS backgrounds, showing that the Lax connection can be gauge transformed to facilitate T-duality and mapping local charges to non-local ones.

Contribution

It demonstrates that the Lax connection's coordinate dependence can be removed via gauge transformation, enabling T-duality of integrable structures in AdS string models.

Findings

T-duality preserves the integrable structure of the sigma model.

Local charges map to non-local charges under T-duality.

The Lax connection can be gauge transformed to be T-dualizable.

Abstract

We discuss an interplay between T-duality and integrability for certain classical non-linear sigma models. In particular, we consider strings on the AdS_5 x S^5 background and perform T-duality along the four isometry directions of AdS_5 in the Poincare patch. The T-dual of the AdS_5 sigma model is again a sigma model on an AdS_5 space. This classical T-duality relation was used in the recently uncovered connection between light-like Wilson loops and MHV gluon scattering amplitudes in the strong coupling limit of the AdS/CFT duality. We show that the explicit coordinate dependence along the T-duality directions of the associated Lax connection (flat current) can be eliminated by means of a field dependent gauge transformation. As a result, the gauge equivalent Lax connection can easily be T-dualized, i.e. written in terms of the dual set of isometric coordinates. The T-dual Lax connection can be used for the derivation of infinitely many conserved charges in the T-dual model. Our construction implies that local (Noether) charges of the original model are mapped to non-local charges of the T-dual model and vice versa.