Noncommutativity in a Time-Dependent Background

TL;DR

This paper calculates a time-dependent noncommutativity parameter in a string theory model with a non-conformal, time-varying background, extending previous work on WZW models with non-semi-simple groups.

Contribution

It introduces a method to derive a time-dependent noncommutativity parameter in a non-conformal, time-dependent background within an open string framework based on a Nappi-Witten type model.

Findings

Derived explicit form of the time-dependent noncommutativity parameter

Extended noncommutative geometry concepts to non-conformal backgrounds

Provided insights into string dynamics in time-varying space-time geometries

Abstract

We compute a time-dependent noncommutativity parameter in a model with a time-dependent background, a space-time metric of the plane wave type supported by a Neveu-Schwarz two-form potential. This model is an open string version of the WZW model based on a non-semi-simple group previously studied by Nappi and Witten. The background we study is not conformally invariant. We consider a light-cone action for the sigma-model, compute the worldsheet propagator, and use it to derive a time-dependent noncommutativity parameter.