Combined fermionic and bosonic T-duality of type II superstring theory with coordinate dependent RR field

TL;DR

This paper explores how fermionic T-duality affects type II superstring theory with coordinate-dependent RR fields, revealing insights into background field transformations and fermionic non-commutativity.

Contribution

It applies the Buscher procedure to analyze fermionic T-duality in the presence of linear RR fields, considering cases with and without bosonic T-dualization, to understand background transformations.

Findings

Transformation laws for background fields under fermionic T-duality.

Conditions for the emergence of fermionic non-commutativity.

Differences in dual actions with and without bosonic T-dualization.

Abstract

We investigate effects of fermionic T-duality on type II superstring in presence of Ramond-Ramond (RR) field that has infinitesimal linear dependence on bosonic coordinate $x^\mu$. Other fields are assumed to be constant. Procedure that we employ for obtaining fermionic T-dual theory is Busher procedure, where we will consider two distinct cases. One, where action has not been T-dualized along bosonic coordinates and other where it has. By analyzing these two cases, their actions and T-dual transformation laws, we obtain some insight into how background fields transform and what are necessary ingredients for emergence of fermionic non-commutativity.