c>1 Non-Critical Strings and Large-N Matrix Field Theory

TL;DR

This paper investigates the phase structure of large-N phi^3 matrix field theory in 1+1 dimensions, providing evidence for non-critical string behavior and analyzing the excitation spectrum and parton distributions.

Contribution

It demonstrates the existence of non-critical string phases in large-N matrix field theory and characterizes their properties using discretised light-cone quantisation and numerical methods.

Findings

Confirmed Polyakov's non-critical string at phase boundary

Found critical exponents consistent with mean field theory

Observed a finite, possibly discrete excitation spectrum

Abstract

Motivated by a possible relativistic string description of hadrons we use a discretised light-cone quantisation and Lanczos algorithm to investigate the phase structure of phi^3 matrix field theory in the large N limit. In 1+1 dimensions we confirm the existence of Polyakov's non-critical string theory at the boundary between parton-like and string-like phases, finding critical exponents for longitudinal oscillations equal to or consistent with those given by a mean field argument. The excitation spectrum is finite, possibly discrete. We calculate light-cone structure functions and find evidence that the probability Q(x) of a parton in the string carrying longitudinal momentum fraction between x and x+dx has support on all 0<x<1, despite the average number of partons being infinite.