Classical Shadows of Higher-Form BRST Anomalies
Abstract
We formulate a precise sense in which a BRST anomaly may possess a classical phase space shadow. It is the non-equivariance class of a Hamiltonian symmetry action on covariant phase space. To organize this statement, we introduce the Weil covariant phase space bicomplex, whose basic subcomplex controls equivariant Hamiltonian lifts. We then compare this purely classical class with local BRST descent. For a Hamiltonian admissible mixed transgression, the ghost-number-two descendant a2d−1 defines a deghostification map to the charge algebra, which is generated by the failure of the Cartan representative to be equivariant. The induced cohomology class is independent of Bardeen type changes of descent representative. Thus the classical anomaly is a shadow of the BRST anomaly in the precise sense that both are realizations of the same Weil transgression class, while remaining objects of different theories. As an explicit example, we analyze a five dimensional inflow transgression and show that the classical charge cocycle and the BRST descendant arise as two realizations of the same Weil transgression class.
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BibTeX
@misc{shen2026classical,
title = {{Classical Shadows of Higher-Form BRST Anomalies}},
author = {Ruizhi Shen and Fu-Wen Shu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36548},
eprint = {2609.36548},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36548},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical Shadows of Higher-Form BRST Anomalies
AU - Ruizhi Shen
AU - Fu-Wen Shu
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36548
UR - https://arxiv.org/abs/2609.36548
AB - We formulate a precise sense in which a BRST anomaly may possess a classical phase space shadow. It is the non-equivariance class of a Hamiltonian symmetry action on covariant phase space. To organize this statement, we introduce the Weil covariant phase space bicomplex, whose basic subcomplex controls equivariant Hamiltonian lifts. We then compare this purely classical class with local BRST descent. For a Hamiltonian admissible mixed transgression, the ghost-number-two descendant a^2_d−1 defines a deghostification map to the charge algebra, which is generated by the failure of the Cartan representative to be equivariant. The induced cohomology class is independent of Bardeen type changes of descent representative. Thus the classical anomaly is a shadow of the BRST anomaly in the precise sense that both are realizations of the same Weil transgression class, while remaining objects of different theories. As an explicit example, we analyze a five dimensional inflow transgression and show that the classical charge cocycle and the BRST descendant arise as two realizations of the same Weil transgression class.
ER -