Partition Function of Chiral Boson on 2-Torus from Floreanini-Jackiw Lagrangian

TL;DR

This paper develops a direct method to compute the partition function of a chiral boson on a torus from the Floreanini-Jackiw Lagrangian, including topological modifications, improving upon traditional path integral approaches.

Contribution

It introduces a novel direct quantization approach for chiral bosons on a torus using modified Lagrangians with topological terms, applicable to interacting theories.

Findings

Correct partition function obtained for free chiral boson

Method applicable to a wider class of interacting theories

Gauge-fixing analysis reproduces known results

Abstract

We revisit the problem of quantizing a chiral boson on a torus. The conventional approach is to extract the partition function of a chiral boson from the path integral of a non-chiral boson. Instead we compute it directly from the chiral boson Lagrangian of Floreanini and Jackiw modified by topological terms involving auxiliary fields. A careful analysis of the gauge-fixing condition for the extra gauge symmetry reproduces the correct results for the free chiral boson, and has the advantage of being applicable to a wider class of interacting chiral boson theories.