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

TL;DR

This paper demonstrates that bosonic and fermionic T-dualizations of type II superstring theory commute and are equivalently represented in double space, linking Buscher's approach with the double space formalism.

Contribution

It establishes the commutativity of bosonic and fermionic T-dualizations and shows their equivalence in double space representation within the pure spinor formulation.

Findings

Bosonic and fermionic T-dualizations commute.

T-dual transformation laws are derived for full dualization.

Buscher approach and double space formalism are shown to be equivalent.

Abstract

In this article I consider type II superstring in the pure spinor formulation with constant background fields in the context of T-dualization. First I 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.