BRST Covariant Phase Space and Holographic Ward Identities

TL;DR

This paper develops a BRST covariant phase space framework to analyze large gauge transformations, their associated charges, and holographic Ward identities, providing new insights into asymptotic symmetries and soft theorems in quantum field theory.

Contribution

It introduces a trigraded BRST covariant phase space and a unified Ward identity for small and large gauge transformations, linking boundary anomalies to holographic symmetries.

Findings

Large gauge transformation charges are shown to be equivalent to classical corner charges.

The boundary Ward identity explains the invariance of the S-matrix under asymptotic symmetries.

Holographic anomalies satisfy a Wess--Zumino consistency condition, clarifying loop corrections to soft theorems.

Abstract

This paper develops an enlarged BRST framework to treat the large gauge transformations of a given quantum field theory. It determines the associated infinitely many Noether charges stemming from a gauge fixed and BRST invariant Lagrangian, a result that cannot be obtained from Noether's second theorem. The geometrical significance of this result is highlighted by the construction of a trigraded BRST covariant phase space, allowing a BRST invariant gauge fixing procedure. This provides an appropriate framework for determining the conserved BRST Noether current of the global BRST symmetry and the associated global Noether charges. The latter are found to be equivalent with the usual classical corner charges of large gauge transformations. It allows one to prove the gauge independence of their physical effects at the perturbative quantum level. In particular, the underlying BRST fundamental canonical relation provides the same graded symplectic brackets as in the classical covariant phase space. A unified Lagrangian Ward identity for small and large gauge transformations is built. It consistently decouples into a bulk part for small gauge transformations, which is the standard BRST--BV quantum master equation, and a boundary part for large gauge transformations. The boundary part provides a perturbation theory origin for the invariance of the Hamiltonian physical $\mathcal{S}$-matrix under asymptotic symmetries. Holographic anomalies for the boundary Ward identity are studied and found to be solutions of a codimension one Wess--Zumino consistency condition. Such solutions are studied in the context of extended BMS symmetry. Their existence clarifies the status of the $1$-loop correction to the subleading soft graviton theorem.