Twist Points as Branch Points for the QCD$_2$ String

TL;DR

This paper demonstrates that the string representation of QCD$_2$ inherently enforces a topological constraint requiring even branch point multiplicities in branched coverings, revealing a fundamental symmetry in the theory.

Contribution

It establishes a topological constraint on branch points in the string representation of QCD$_2$ and related Yang-Mills theories, based on Young-tableau symmetry.

Findings

String representation satisfies even branch point multiplicity constraint.

Topological symmetry applies to both orientable and nonorientable surfaces.

Results extend to $ ext{SO}(N)$ and $ ext{Sp}(N)$ Yang-Mills$_2$ theories.

Abstract

We show that the string representation of the QCD$_2$ partition function satisfies, by virtue of a Young-tableau-transposition symmetry, the topological constraint that any branched covering of an orientable or nonorientable surface without boundary must have an {\em even} branch point multiplicity. This statement holds for each chiral sector and requires multiple branch point behavior for the twist points, since cross-terms appear that couple twist points with odd powers of simple branch points. We obtain the same result for the complete partition function of $\son$ and $\spn$ Yang-Mills$_2$ theory.