Hamiltonian BRST formalism for gauge fields on black hole spacetimes

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 ($\Lambda \ge 0$). 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.

arXiv comment28 pp

References in corpus (28)

• Soft Hair on Black Holes
• BMS supertranslations and Weinberg's soft graviton theorem
• New Symmetries of Massless QED
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Superrotation Charge and Supertranslation Hair on Black Holes
• Entanglement entropy: holography and renormalization group
• Entanglement entropy of electromagnetic edge modes
• Infrared Divergences in QED, Revisited
• Geometric entropy and edge modes of the electromagnetic field
• Symmetries and charges of general relativity at null boundaries
• Charges from Dressed Matter: Construction
• Null Conservation Laws for Gravity
• A New Symmetry for QED
• Edge Dynamics from the Path Integral: Maxwell and Yang-Mills
• Charges from Dressed Matter: Physics and Renormalisation
• Boundary Conditions as Dirac Constraints
• Horizon Shells and BMS-like Soldering Transformations
• BRST Invariant Boundary Conditions for Gauge Theories
• Edge State Quantization: Vector Fields in Rindler
• The Edge States of the BF System and the London Equations
• Maxwell-Chern-Simons Electrodynamics on a Disk
• Hamiltonian systems with boundaries
• Chern-Simons Duality and the Quantum Hall Effect
• Unitarity of Maxwell theory on curved spacetimes in the covariant formalism
• Black hole entropy from non-proper gauge degrees of freedom: II. The charged vacuum capacitor
• BRST-invariant boundary conditions and strong ellipticity
• Constrained field theories on spherically symmetric spacetimes with horizons
• Constrained field theories on Kerr backgrounds