Unifying Approaches to Chiral Bosons

TL;DR

This paper presents a unified framework for chiral bosons, connecting various formulations through a Chern-Simons perspective, and extends the theory to non-Abelian and twisted self-dual cases relevant in string theory.

Contribution

It introduces a novel approach linking different chiral boson formulations and generalizes to non-Abelian and twisted self-dual chiral bosons in two dimensions.

Findings

Unified approach to chiral bosons via Chern-Simons theory

Extension to non-Abelian chiral bosons in 2D

Inclusion of twisted self-duality relevant for T-duality

Abstract

Chiral bosons, or self-dual p-form fields, are ubiquitous in string theoretic contexts but are challenging to treat. Lagrangian constructions invariably introduce a complexity be it auxiliary fields or sacrificing Lorentz invariance. In this note we show how to pass between such different approaches to chiral bosons starting from a Chern Simons point of view to recover formulations of Pasti, Sorokin and Tonin and of Mkrtchyan. This leads to a novel generalisation of the latter to include non-Abelian chiral bosons in 2-dimensions, and generalisations to include twisted self-duality which are relevant in T-duality symmetric approaches to string theory. Our approach also shows how global affine symmetries of two- and higher-dimensional chiral bosons emerge from broken Chern-Simons gauge transformations on the boundary.