BRST symmetry and $W$-algebra in higher derivative models

TL;DR

This paper explores the relationship between BRST symmetries and W-algebras in higher derivative relativistic particle models, revealing how these symmetries form an algebraic structure and can be manipulated via finite coordinate-dependent transformations.

Contribution

It establishes the connection between BRST symmetries and W-algebra in higher derivative models and introduces a method to connect different gauges using finite coordinate-dependent BRST transformations.

Findings

Full W-algebra emerges with anti-BRST and BRST combined

Finite coordinate-dependent BRST changes gauge-fixing fermion

Connection between different gauge conditions demonstrated

Abstract

In this paper we discuss the (anti-)BRST symmetries and $W$-algebra of higher derivative theories of relativistic particles satisfying general gauge conditions. Using this formalism, the connection between the (anti-)BRST symmetries and $W$-algebra for the rigid relativistic particle is established. Incidentally, the full $W$-algebra emerges only when the anti-BRST transformations are considered in tandem with the BRST ones. Further, the BRST symmetry is made finite and coordinate-dependent. We show that such finite coordinate-dependent BRST symmetry changes the BRST invariant gauge-fixing fermion within the functional integration. This is exploited to connect two different arbitrary gauge conditions.