The model for self-dual chiral bosons as a Hodge theory

TL;DR

This paper models a (1+1) dimensional self-dual chiral boson as a gauge theory, demonstrating its symmetries correspond to de Rham cohomological operators and exploring Hodge decomposition within this framework.

Contribution

It establishes a connection between the symmetries of a self-dual chiral boson and Hodge theory, providing a novel geometric interpretation of gauge symmetries.

Findings

Nilpotent charges satisfy de Rham cohomology algebra

Hodge decomposition theorem is applicable to the model

Symmetry transformations include BRST, anti-BRST, co-BRST, anti co-BRST

Abstract

We consider (1+1) dimensional theory for a single self-dual chiral boson as classical model for gauge theory. Using Batalin-Fradkin-Vilkovisky (BFV) technique the nilpotent BRST and anti BRST symmetry transformations for this theory have been studied. In this model other forms of nilpotent symmetry transformations like co-BRST and anti co-BRST which leave the gauge-fixing part of the action invariant, are also explored. We show that the nilpotent charges for these symmetry transformations satisfy the algebra of de Rham cohomological operators in differential geometry. The Hodge decomposition theorem on compact manifold is also studied in the context of conserved charges.