Double space T-dualization and coordinate dependent RR

TL;DR

This paper explores T-dualization in double space formalism of type II superstring theory with coordinate-dependent Ramond-Ramond fields, demonstrating equivalence with Buscher's approach when background fields depend on coordinates.

Contribution

It extends double space T-dualization to include coordinate-dependent Ramond-Ramond fields and shows its equivalence to Buscher's method under these conditions.

Findings

Double space T-dualization formalism applied to coordinate-dependent RR fields.

T-duality transformations represented as permutations of coordinates.

Equivalence established between double space and Buscher T-dualization methods.

Abstract

In this article we examine T-dualization in double space formalism of type II superstring theory in pure spinor formulation. Background fields that we consider will all be constant except Ramond-Ramond field which will infinitesimally depend only on bosonic coordinates $x^\mu$. In double space T-dual transformations are represented as permutations between starting $x^\mu$ and dual coordinates $y_\mu$. Combining these two sets of coordinates into double coordinate $Z^M = (x^\mu, y_\mu)$ while demanding that T-dual double coordinates have same transformation laws, we obtain how background fields transform under T-duality. Comparing these results with ones obtained with Buscher T-dualization procedure we are able to conclude that these two approaches are equivalent for cases where background fields have coordinate dependence.