BRST quantization and equivariant cohomology: localization with asymptotic boundaries

Bernard de Wit, Sameer Murthy, Valentin Reys*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)
179 Downloads (Pure)


We develop BRST quantization of gauge theories with a soft gauge algebra on spaces with asymptotic boundaries. The asymptotic boundary conditions are imposed on background fields, while quantum fluctuations about these fields are described in terms of quantum fields that vanish at the boundary. This leads us to construct a suitable background field formalism that is generally applicable to soft gauge algebras, and therefore to supergravity. We define a nilpotent BRST charge that acts on both the background and the quantum fields, as well as on the background and quantum ghosts. When the background is restricted to be invariant under a residual isometry group, the background ghosts must be restricted accordingly and play the role of the parameters of the background isometries. Requiring in addition that the background ghosts will be BRST invariant as well then converts the BRST algebra into an equivariant one. The background fields and ghosts are then invariant under the equivariant transformations while the quantum fields and ghosts transform under both the equivariant and the background transformations. We demonstrate how this formalism is suitable for carrying out localization calculations in a large class of theories, including supergravity defined on asymptotic backgrounds that admit supersymmetry.

Original languageEnglish
Article number84
JournalJournal of High Energy Physics
Issue number9
Publication statusPublished - 17 Sept 2018


  • BRST Quantization
  • Gauge Symmetry
  • Supergravity Models
  • Supersymmetric Gauge Theory


Dive into the research topics of 'BRST quantization and equivariant cohomology: localization with asymptotic boundaries'. Together they form a unique fingerprint.

Cite this