DLCQ and Plane Wave Matrix Big Bang Models

TL;DR

This paper extends the DLCQ and matrix big bang models to curved plane wave backgrounds, analyzing their symmetries, singularities, and resulting matrix string theories with a focus on strong coupling effects and tachyonic instabilities.

Contribution

It introduces a detailed analysis of DLCQ in curved plane wave spacetimes and explores the resulting matrix string theories, including concrete examples with IIA backgrounds.

Findings

Singular homogeneous plane waves serve as models for space-time singularities.

Strong coupling singularities relate to world-sheet tachyonic modes.

Explicit analysis of IIA plane wave backgrounds with null dilaton.

Abstract

We study the generalisations of the Craps-Sethi-Verlinde matrix big bang model to curved, in particular plane wave, space-times, beginning with a careful discussion of the DLCQ procedure. Singular homogeneous plane waves are ideal toy-models of realistic space-time singularities since they have been shown to arise universally as their Penrose limits, and we emphasise the role played by the symmetries of these plane waves in implementing the flat space Seiberg-Sen DLCQ prescription for these curved backgrounds. We then analyse various aspects of the resulting matrix string Yang-Mills theories, such as the relation between strong coupling space-time singularities and world-sheet tachyonic mass terms. In order to have concrete examples at hand, in an appendix we determine and analyse the IIA singular homogeneous plane wave - null dilaton backgrounds.