Danijel Obric | Searcharxiv

arXiv2022

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

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 $x^μ$. 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.

hep-th↗

arXiv2022

Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field

In this paper we will consider noncommutativity that arises from bosonic T-dualization of type II superstring in presence of Ramond-Ramond (RR) field, which linearly depends on the bosonic coordinates $x^μ$. The derivative of the RR field $C^{αβ}_μ$ is infinitesimal. We will employ generalized Buscher procedure that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T-dual theory is non-local. It is defined in non-geometric space spanned by Lagrange multipliers $y_μ$. We will apply generalized Buscher procedure once more on T-dual theory and prove that original theory can be salvaged. Finally, we will use T-dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T-dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates $x^μ$, $θ^α$ and $\barθ^α$, while nonassociativity parameter is a constant tensor containing infinitesimal $C^{αβ}_μ$.

hep-th↗