On the holomorphically factorized partition function for abelian gauge theory in six dimensions

TL;DR

This paper derives the partition functions for an abelian two-form chiral gauge field on a six-torus using holomorphic factorization, identifying the unique modular invariant partition function consistent with previous Hamiltonian results.

Contribution

It demonstrates that among the holomorphically factorized partition functions, only one is modular invariant, aligning with earlier Hamiltonian formulations.

Findings

Exactly one partition function is modular invariant.

The modular invariant partition function matches previous Hamiltonian results.

Holomorphic factorization effectively determines the partition function structure.

Abstract

We use holomorphic factorization to find the partition functions of an abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that previously has been found in a hamiltonian formulation.