A Path Integral for the Chiral-Form Partition Function

TL;DR

This paper develops a path integral approach for the chiral-form partition function on a torus, using a Wick-rotation method, and extends results to higher-dimensional chiral forms.

Contribution

It introduces a novel path-integral formulation for chiral bosons and forms, utilizing a Wick-rotation from a complex metric deformation, aligning with expected theta function properties.

Findings

Reproduces known partition function characteristics for chiral bosons

Extends the approach to six-dimensional chiral 2-forms

Provides a framework applicable to 4k+2 dimensions

Abstract

Starting from the recent action proposed by Sen [1,2], we evaluate the partition function of the compact chiral boson on a two-dimensional torus using a path-integral formulation. Crucially, we use a Wick-rotation procedure obtained from a complex deformation of the physical spacetime metric. This directly reproduces the expected result including general characteristics for the theta functions. We also present results for the chiral 2-form potential in six dimensions which can be readily extended to 4k+2 dimensions.