Light-cone approach to random surfaces embedded in two dimensions

TL;DR

This paper reviews a light-cone quantization method for matrix models related to 2D quantum gravity, deriving a Schrödinger equation for the string spectrum and analyzing its properties near criticality.

Contribution

It introduces a light-cone approach to matrix models for 2D quantum gravity and derives a Schrödinger equation for the free string spectrum in the large N limit.

Findings

Spectrum appears tachyonic near critical point

String tension diverges at the critical point

Numerical analysis supports the theoretical predictions

Abstract

We review the recently proposed \lc\ quantization of the matrix model which is expected to have a critical point describing 2-d quantum gravity coupled to $c=2$ matter. In the $N\to\infty$ limit, we derive a linear Schroedinger equation for the free string spectrum. Numerical study of this equation suggests that the spectrum is tachyonic, and that the string tension diverges at the critical point.