Simultaneous bosonic and fermionic T-dualization of the type II superstring theory - Buscher approach and double space representation

TL;DR

The paper addresses simultaneous bosonic and fermionic T-duality for type II superstrings in the pure spinor formulation with constant backgrounds, showing that the two dualities commute and deriving the full T-dual transformation laws. It demonstrates this equivalence through both the analytic Buscher procedure and a double-space representation, where a single permutation of doubled coordinates yields the full dual theory and its two chiral generalized metrics reproduce the Buscher results. The main contributions are the explicit full dual background fields, the verified commutativity of dualization sequences, and a coherent double-space framework that matches the Buscher approach. This work reinforces the consistency of dualities in the pure spinor setting and provides a robust method for encoding full duality in double space, potentially facilitating further explorations of dual backgrounds in curved or more general backgrounds.

Abstract

In this article we consider type II superstring in the pure spinor formulation with constant background fields in the context of T-dualization. First we prove that bosonic and fermionic T-dualization commute using already known T-dual transformation laws for bosonic and fermionic T-dualization. Consequently, the T-dual transformation laws of the full T-dualization are obtained. At the end the full T-dualization is realized in double space and it is showed that Buscher procedure and double space approach are equivalent in this specific case.