Anomalies in Covariant Fracton Theories

TL;DR

This paper investigates anomalies in covariant fracton theories with symmetric tensor gauge fields, using BRST cohomology, and identifies the most general anomalies in various dimensions, illustrating with a higher-derivative scalar field example.

Contribution

It computes the possible anomalies in covariant fracton theories across different dimensions using BRST cohomology, revealing their dependence on gauge fields and parameters.

Findings

Most general anomalies in 2D and 4D covariant fracton theories identified.

Anomalies depend only on background gauge fields and parameters.

A higher-derivative scalar field exemplifies covariant fracton matter.

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.