Two-Dimensional Yang-Mills Theory on Surfaces With Corners in Batalin-Vilkovisky Formalism

TL;DR

This paper demonstrates how the non-perturbative partition function of 2D Yang-Mills theory can be derived from perturbative path integrals on surfaces with boundaries and corners using the BV-BFV formalism, emphasizing the role of cutting and gluing techniques.

Contribution

It develops a method to recover the non-perturbative partition function of 2D Yang-Mills from perturbative calculations within the BV-BFV formalism on surfaces with corners.

Findings

Partition function recovered from perturbative path integrals.

Gluing of surface pieces reproduces known non-perturbative results.

Formalism applicable to surfaces with boundaries and corners.

Abstract

In this paper we recover the non-perturbative partition function of 2D~Yang-Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D~Yang-Mills theory on surfaces with boundaries and corners in the Batalin-Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting -- the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces -- building blocks -- and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D~Yang-Mills theory.