Simultaneous T-dualization of type II pure spinor superstring

TL;DR

This paper develops a comprehensive method for performing simultaneous T-dualization of type II superstring actions in pure spinor formulation, deriving explicit transformations of background fields and the dilaton.

Contribution

It provides the full form of T-dual background fields, transformation laws, and the T-dual dilaton in the pure spinor superstring framework, considering simultaneous T-dualization along multiple coordinates.

Findings

Derived explicit T-dual background fields and transformation laws.

Obtained the full expression for the T-dual dilaton field.

Addressed the transformation of two chiral sectors with different vielbeins and gamma matrices.

Abstract

In this article we consider simultaneous T-dualization of type II superstring action in pure spinor formulation. Simultaneous T-dualization means that we make T-dualization at the same time along some subset of initial coordinates marked by $x^a$. The only imposed assumption stems from the applicability of the Buscher T-dualization procedure - background fields do not depend on dualized directions $x^a$. In this way we obtain the full form of the T-dual background fields and T-dual transformation laws. Because two chiral sectors transform differently, there are two sets of vielbeins and gamma matrices connected by the local Lorentz transformation. Its spinorial representation is the same as in the constant background case. We also found the full expression for T-dual dilaton field.