Aspects of Plane Wave (Matrix) String Dynamics

TL;DR

This paper clarifies the use of Brinkmann variables over Rosen variables in quantum plane wave string theories and discusses regularization techniques for singular plane waves, enhancing understanding of string dynamics in these backgrounds.

Contribution

It conclusively establishes the preference for Brinkmann variables in quantum theory and analyzes regularization methods for singular plane wave metrics.

Findings

Brinkmann variables are superior for quantum analysis of plane wave backgrounds.

Regularization methods can mitigate singularities in plane wave metrics.

Discussion of benefits and limitations of different regularization techniques.

Abstract

We analyse two issues that arise in the context of (matrix) string theories in plane wave backgrounds, namely (1) the use of Brinkmann- versus Rosen-variables in the quantum theory for general plane waves (which we settle conclusively in favour of Brinkmann variables), and (2) the regularisation of the quantum dynamics for a certain class of singular plane waves (discussing the benefits and limitations of regularisations of the plane-wave metric itself).