Abstract
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.
Highlights
When the background is restricted to be invariant under a residual isometry group, the background ghosts must be restricted and play the role of the parameters of the background isometries
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
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
Summary
To introduce our notation we first define the BRST transformations in the generic case of a gauge theory of bosonic gauge transformations with a gauge algebra that closes off shell (i.e. without the need of imposing the field equations). Where R(φ)iα may include derivatives acting on the parameters ξα(x) and may depend non-linearly on the fields φi They must satisfy the general closure relation δ(ξ1) δ(ξ2) − δ(ξ2) δ(ξ1) = δ(ξ3) ,. In addition we must include an extra BRST invariant term denoted by Lg.f. to fix the gauge, which will provide the ghost-dependent terms in the full quantum action. This requires the introducion of anti-ghost fields bα and Lagrange multiplier fields Bα, which will transform under nilpotent BRST transformations that we will define momentarily. In that case the ghost system will have a secondary gauge invariance which must be fixed by repeating the same procedure and introducing a generation of ghost fields. Means that, when considering theories with both bosonic and fermionic generators, one cannot just copy the results from this paper, because we may have accidentally ordered the terms in a way that is allowed for the purely bosonic case, but not for the mixed case
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
