Green-Schwarz Strings in TsT-transformed backgrounds

TL;DR

The paper develops a universal method to derive the Green-Schwarz string action in TsT-transformed backgrounds, showing that integrability is preserved and providing explicit boundary conditions and monodromy matrix expressions for deformed AdS_5 x S^5.

Contribution

It introduces a general procedure to obtain the Green-Schwarz action in TsT backgrounds, demonstrating the preservation of integrability and detailing boundary conditions and monodromy matrices.

Findings

TsT transformations relate isometry variables universally.

Strings in TsT backgrounds are described by twisted boundary conditions.

Integrability of the string sigma model is preserved under TsT transformations.

Abstract

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial background in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted boundary conditions. Our construction implies that a TsT transformation preserves integrability properties of the string sigma model. We discuss in detail type IIB strings propagating in the \g_i-deformed AdS_5 x S^5 space-time, find the twisted boundary conditions for bosons and fermions, and use them to write down an explicit expression for the monodromy matrix. We also discuss string zero modes whose dynamics is governed by a fermionicgeneralization of the integrable Neumann model.