Noncommutativity and Nonassociativity of Type II Superstring with Coordinate Dependent RR Field

Abstract

AbstractIn 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 . The derivative of the RR field 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 . 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 , and , while nonassociativity parameter is a constant tensor containing infinitesimal .