Two Dimensional QCD is a String Theory
David J. Gross, Washington Taylor
TL;DR
The paper builds a concrete map-based interpretation of 2D QCD by showing that its 1/N expansion coefficients correspond to sums over branched covers of the target manifold, effectively realizing QCD2 as a two-dimensional string theory. It develops a two-part framework: a chiral-sector decomposition connected to orientation-preserving covers and a geometric account of subleading corrections via tubes and collapsed handles, with a complete torus case and partial insights for higher-genus targets. It further demonstrates a plaquette-based derivation that is compatible with gluing to yield coverings of any orientable manifold and discusses non-orientable targets. The work suggests a string action that suppresses folds and outlines future directions, including fermions and extensions to higher dimensions.
Abstract
The partition function of two dimensional QCD on a Riemann surface of area $A$ is expanded as a power series in $1/N$ and $A$. It is shown that the coefficients of this expansion are precisely determined by a sum over maps from a two dimensional surface onto the two dimensional target space. Thus two dimensional QCD has a simple interpretation as a closed string theory.