A Matrix Model for the Null-Brane

TL;DR

This work confronts the problem of cosmological singularities in string theory by constructing a DLCQ (null) description of the null-brane background as a time-dependent matrix model. It provides an explicit abelian D0-brane DBI action on the null-brane and a conjectured non-abelian DLCQ Lagrangian for $N$ D0-branes, showing that the system behaves like Matrix-string theory near $\tau=0$ and flows to quantum mechanics for large $|\tau|$. The results offer a nonperturbative framework to study null time and the string S-matrix in a controlled, cosmology-inspired setting and lay groundwork for higher-dimensional generalizations and holographic interpretations.

Abstract

The null-brane background is a simple smooth 1/2 BPS solution of string theory. By tuning a parameter, this background develops a big crunch/big bang type singularity. We construct the DLCQ description of this space-time in terms of a Yang-Mills theory on a time-dependent space-time. Our dual Matrix description provides a non-perturbative framework in which the fate of both (null) time, and the string S-matrix can be studied.

Figures (1)

• Figure 1: The circle radius shrinks to a minimum $L$ at $x^+ =0$.