Hamiltonian BRST formalism for gauge fields on black hole spacetimes

TL;DR

This paper extends the BRST formalism to gauge fields on black hole spacetimes, revealing horizon contributions to constraints, ghost actions, and gauge invariants, with implications for quantum field theory in curved backgrounds.

Contribution

It develops a Hamiltonian BRST framework incorporating horizon surface terms, introduces a radiation-like gauge at horizons, and constructs co-BRST symmetry for gauge invariance on black hole backgrounds.

Findings

Horizon surface terms modify Gauss law constraints.

Ghost and gauge fixing actions include horizon surface integrals.

Dressed gauge-invariant fields are affected by Killing horizons.

Abstract

We investigate the Becchi-Rouet-Stora-Tyutin (BRST) formalism for gauge theories on spherically symmetric black hole spacetimes, with or without a cosmological constant ($\Lambda\geq0$). This is illustrated through the example of scalar electrodynamics. We first demonstrate that the horizons contribute additional surface terms to the Gauss law constraint of the theory when gauge transformations are not required to vanish on the horizons. We then consider the BRST invariant path integral including these surface terms following the Hamiltonian BRST formalism. We fix a radiation-like gauge which involves null components of the electromagnetic field at the horizons. We find that the presence of the surface terms in the constraint forces the ghost and gauge fixing actions to include additional surface integrals at the horizons. The null combination of the gauge fields at the horizons is shown to modify the ghost number charge of the theory through additional terms at the horizons. We also demonstrate how one can construct a gauge-fixing fermion which generates its own nilpotent symmetry transformations, called co-BRST transformations, that leave the theory invariant. The BRST and co-BRST transformations are further used to identify dressed (gauge invariant) fields of theory, whose dressings are affected by the presence of Killing horizons. We conclude with a discussion of potential applications of our results in soft limits and thermal field theories on black hole backgrounds.