Anomalies in Covariant Fracton Theories

Abstract

Covariant (Lorentz invariant) fracton matter, minimally coupled and charged under a symmetric rank two gauge tensor, is considered. The gauge transformations correspond to linearized longitudinal diffeomorphisms. Consistent possible anomalies are computed using the BRST cohomology method. They depend only on the gauge field, treated as a background field, and on the gauge parameter, promoted to an anticommuting scalar ghost field. The problem is phrased in terms of polyforms, whose total degree is the sum of the form degree and of the ghost number. The most general anomaly in two dimensions and in four dimensions is computed and an anomaly in arbitrary dimensions is individuated. In conclusion, it is shown that a simple higher-derivative scalar field theory is an example of covariant fracton matter.

Published version: comments and references added, minor corrections

References in corpus (9)

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Cited by in corpus (6)

• Covariant Interacting Fractons
• Covariant field theory of 3D massive fractons
• Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes
• Covariant Fractons and Weitzenböck Torsion
• Emergent fracton strings from covariant bi-form gauge field theory
• Kodaira-Spencer Anomalies with Stora-Zumino Method