Two-dimensional Yang-Mills Theory on Recursive Infinite Genus Surfaces

TL;DR

This paper develops a recursive method to compute the partition function of 2D Yang-Mills theory on infinite genus surfaces, extending to quantum deformed cases, revealing new computational techniques for complex topologies.

Contribution

It introduces a recursive approach to calculate Yang-Mills partition functions on infinite genus surfaces, including quantum deformations, expanding the understanding of gauge theories on complex topologies.

Findings

Partition functions computed for infinite genus surfaces.

Method applicable to quantum deformed Yang-Mills theory.

Recursive structure simplifies complex topological calculations.

Abstract

The partition function of Euclidean Yang-Mills theory on two dimensional surfaces is given by the Migdal formula. It involves the area and topological characteristics of the surface. We consider this theory on a class of infinite genus surfaces that are constructed recursively. We make use of this recursive structure to compute the partition functions (with or without additional Wilson loops) on such surfaces. Our method also works for the quantum deformed Yang-Mills theory.