BV and BFV Formulation of a Gauge Theory of Quadratic Lie Algebras in 2-d and a Construction of W3 Topological Gravity

TL;DR

This paper applies a generalized BV method to a 2D gauge theory based on quadratic Lie algebras, compares BRST charges from different formalisms, and constructs a W3 topological gravity using the W3 algebra.

Contribution

It introduces a novel application of the generalized BV method to quadratic Lie algebra gauge theories and constructs a W3 topological gravity in 2D.

Findings

BRST charges from BV and BFV methods coincide

Constructed a W3 topological gravity in 2D

Discussed gauge fixing of the W3 gravity

Abstract

The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in 2-dimensions. The charge corresponding to BRST symmetry derived from this solution in terms of the phase space variables by using the Noether procedure, and the one found due to the BFV-method are compared and found to coincide. $W_3$ algebra, formulated in terms of a continuous variable is emploied in the mentioned gauge theory to construct a $W_3$ topological gravity. Moreover, its gauge fixing is briefly discussed.