Two Dimensional QCD as a String Theory

TL;DR

The work addresses whether ${\rm QCD}_2$ admits a string theory description by computing the partition function on arbitrary 2D manifolds and performing a controlled $1/N$ expansion. Using a heat-kernel lattice regularization, the author derives an exact expression for the genus-$G$ partition function and shows the expansion contains only even powers of $1/N$, consistent with a sum over (branched) maps between surfaces. Detailed comparisons for genus $G>1$, the torus, and the sphere reveal explicit connections to map-counting via covering maps and modular functions, notably a Dedekind eta structure on the torus. These results provide strong, nonperturbative evidence for a string representation of ${\rm QCD}_2$ and outline a path toward reconstructing the corresponding string action and extending the approach to more realistic theories.

Abstract

I explore the possibility of finding an equivalent string representation of two dimensional QCD. I develop the large N expansion of the ${\rm QCD_2}$ partition function on an arbitrary two dimensional Euclidean manifold. If this is related to a two-dimensional string theory then many of the coefficients of the ${1\over N}$ expansion must vanish. This is shown to be true to all orders, giving strong evidence for the existence of a string representation.