Boson-Fermion Correspondence and Holomorphic Anomaly Equation in 2d Yang-Mills Theory on Torus

TL;DR

This paper derives and proves a holomorphic anomaly equation for 2d Yang-Mills theory on a torus using boson-fermion correspondence, linking bosonic and fermionic formulations of the partition function.

Contribution

It introduces a fermionic derivation of the deformed partition function and provides a proof of the holomorphic anomaly equation in this context.

Findings

Derived the fermionic formula for the deformed partition function

Proved the holomorphic anomaly equation using boson-fermion correspondence

Connected bosonic and fermionic descriptions of 2d Yang-Mills partition function

Abstract

Recently, Okuyama and Sakai proposed a novel holomorphic anomaly equation for the partition function of 2d Yang-Mills theory on a torus, based on an anholomorphic deformation of the propagator in the bosonic formulation. Using the boson-fermion correspondence, we derive the formula for the deformed partition function in fermionic description and give a proof of the holomorphic anomaly equation.