On Matrix Strings, the Large N Limit and Discretized Light-Cone Quantization

TL;DR

This paper explores a supersymmetric matrix field theory derived from super Yang-Mills, using light-cone quantization and a double scaling limit to connect gauge theory with string dynamics in a non-perturbative framework.

Contribution

It introduces a double scaling limit involving N and K that reveals an effective string coupling, unifying string and Yang-Mills theories in a discretized light-cone quantization setting.

Findings

Double scaling limit implies an effective string coupling.

Framework unifies string dynamics with Yang-Mills theory.

Quantization via DLCQ provides a natural approach for non-perturbative analysis.

Abstract

We consider the 1+1 dimensional supersymmetric matrix field theory obtained from a dimensional reduction of ten dimensional ${\cal N} = 1$ super Yang-Mills, which is a matrix model candidate for non-perturbative Type IIA string theory. The gauge group here is U($N$), where $N$ is sent to infinity. We adopt light-cone coordinates to parametrize the string world sheet, and choose to work in the light-cone gauge. Quantizing this theory via Discretized Light-Cone Quantization (DLCQ) introduces an integer, K, which restricts the light-cone momentum-fraction of constituent quanta to be integer multiples of 1/K. We show how a double scaling limit involving the integers $K$ and $N$ implies the existence of an extra (free) parameter in the Yang-Mills theory, which plays the role of an effective string coupling constant. The formulation here provides a natural framework for studying quantitatively string dynamics and conventional Yang-Mills in a unified setting.