Dirichlet boundary conditions in type IIB superstring theory and fermionic T-duality

TL;DR

This paper explores how Dirichlet boundary conditions induce noncommutativity in momenta and examines the relationship between fermionic T-duality and background fields in type IIB superstring theory, revealing that momenta become noncommutative while coordinates commute.

Contribution

It establishes a connection between Dirichlet boundary conditions, noncommutativity, and fermionic T-duality in type IIB superstring theory, using a formalism that treats fermionic variables similarly to bosonic ones.

Findings

Momenta become noncommutative under Dirichlet boundary conditions.

Fermionic T-dual fields correspond to noncommutativity parameters.

Effective metric remains unchanged, and the effective Kalb-Ramond field vanishes.

Abstract

In this article we investigate the relation between consequences of Dirichlet boundary conditions (momenta noncommutativity and parameters of the effective theory) and background fields of fermionic T-dual theory. We impose Dirichlet boundary conditions on the endpoints of the open string propagating in background of type IIB superstring theory with constant background fields. We showed that on the solution of the boundary conditions the momenta become noncommutative, while the coordinates commute. Fermionic T-duality is also introduced and its relation to noncommutativity is considered. We use compact notation so that type IIB superstring formally gets the form of the bosonic one with Grassman variables. Then momenta noncommutativity parameters are fermionic T-dual fields. The effective theory, the initial theory on the solution of boundary conditions, is bilinear in the effective coordinates, odd under world-sheet parity transformation. The effective metric is equal to the initial one and terms with the effective Kalb-Ramond field vanish.