Partition functions of chiral gauge theories on the two dimensional torus and their duality properties

TL;DR

This paper computes partition functions of two families of abelian chiral gauge theories on a torus, revealing duality properties and conditions for unitarity, with implications for nonabelian theories.

Contribution

It provides explicit partition function calculations for abelian chiral gauge theories on the torus, uncovering an exact duality and testing consistency of anomalous gauge theories.

Findings

Unitarity is recovered in specific parameter regions.

Effective dynamics relate to fermionic interacting models.

An exact duality is identified for the first family.

Abstract

Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An explicit computation of the partition functions shows that unitarity is recovered in particular regions of parameter space and that the effective dynamics is described in terms of fermionic interacting models. For the first family, this connection with fermionic models uncovers an exact duality which is conjectured to hold in the nonabelian case as well.