Pure Spinor Strings in TsT Deformed Background

TL;DR

This paper studies pure spinor superstrings in TsT-deformed backgrounds, showing how their actions relate to the original background with twisted boundary conditions and analyzing conditions for quantum conformal invariance.

Contribution

It constructs the pure spinor action in TsT backgrounds with manifest U(1) symmetry and analyzes the implications for quantum conformal invariance and integrability.

Findings

Pure spinor action can be expressed with manifest U(1) isometry.

Twisted boundary conditions affect quantum conformal invariance.

Lax pair for TsT-transformed background is derived.

Abstract

We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsT-transformed background are related to the isometry variables of the initial background in the universal way that is independent of the details of the background. We will argue that after redefinitions of pure spinors and the fermionic variables we can construct pure spinor action with manifest U(1) isometry. This fact implies that the pure spinor string in TsT-transformed background is described by pure spinor string in the original background where world-volume modes are subject to twisted boundary conditions. We will argue that these twisted boundary conditions generally prevent to prove the quantum conformal invariance of the pure spinor string in AdS_5 x S^5 background. We determine the conditions under which this quantum conformal invariance can be proved. We also determine the Lax pair for pure spinor strings in the TsT-transformed background.