The Seiberg-Witten Map for a Time-dependent Background

TL;DR

This paper investigates the Seiberg-Witten map in a time-dependent null-brane background, analyzing its Lie algebra structure and the relation between different star products, advancing understanding of noncommutative geometries in string theory.

Contribution

It provides a detailed study of the Seiberg-Witten map for a dynamic background and compares the Kontsevich and Weyl-Moyal star products in this context.

Findings

The coordinates exhibit linear Lie algebra-type noncommutativity.

The equivalence between Kontsevich and Weyl-Moyal star products is established.

Insights into noncommutative structures in time-dependent string backgrounds.

Abstract

In this paper the Seiberg-Witten map for a time-dependent background related to a null-brane orbifold is studied. The commutation relations of the coordinates are linear, i.e. it is an example of the Lie algebra type. The equivalence map between the Kontsevich star product for this background and the Weyl-Moyal star product for a background with constant noncommutativity parameter is also studied.