Light-Cone Quantization of the c=2 Matrix Model

TL;DR

This paper investigates the large N limit of a 2D matrix field theory using light-cone quantization, revealing potential continuous string spectra and implications for 3D string dynamics.

Contribution

It introduces a light-cone quantization approach for the c=2 matrix model, showing how discretized longitudinal momenta lead to finite matrix spectra and suggesting a transition to continuous spectra at critical coupling.

Findings

Numerical results indicate a continuous string spectrum at critical coupling.

Discretized longitudinal momenta reduce spectrum calculation to finite matrix diagonalization.

Potential emergence of a third dimension in string theory via Liouville mode dynamics.

Abstract

We study the large $N$ limit of an interacting \td\ matrix field theory, whose perturbative expansion generates the sum over planar random graphs embedded in two dimensions. In the \lc\ quantization the theory possesses closed string excitations which become free as $N\to\infty$. If the longitudinal momenta are discretized, then the calculation of the free string spectrum reduces to finite matrix diagonalization, the size of the matrix growing as the cut-off is removed. Our numerical results suggest that, for a critical coupling, the \lc\ string spectrum becomes continuous. This would indicate the massless dynamics of the Liouville mode of \td\ gravity, which would constitute a {\it third} dimension of the string theory.