Non-Quadratic Gauge Fixing and Ghosts for Gauge Theories on the Hypersphere

TL;DR

This paper explores non-quadratic gauge fixing in gauge theories on a hypersphere, revealing a complex ghost structure that differs from traditional quadratic approaches.

Contribution

It introduces a novel non-quadratic gauge fixing Lagrangian and derives the associated ghost action, expanding understanding of gauge fixing on curved manifolds.

Findings

Two pairs of complex Fermionic ghosts identified

Two Bosonic real ghosts identified

Non-quadratic gauge fixing alters ghost structure

Abstract

It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this non-quadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.