Gauging in superconductors and other electronic systems

TL;DR

This paper uses topological field theories and generalized symmetries to describe superconductors as topological phases with unique global features, anomalies, and implications beyond traditional models.

Contribution

It provides an updated theoretical framework for superconductors, highlighting their topological order, fermionic origins, and associated anomalies in various dimensions.

Findings

Superconductors can be described by BF theory at low energies.

Gauging fermion parity reveals a gravito-magnetic anomaly.

The anomaly constrains trivial phases and applies beyond the Higgs model.

Abstract

Ordinary, s-wave superconductors have been recognized as being topological phases of matter, in which the dynamical gauge field implies less understood global features. Using the tools of topological field theories and generalized symmetries, we provide an updated description of these systems. At very low energies, the Higgs model reduces to the BF theory, which exhibits topological order. Furthermore, the gauge field must be a spin$_c$ connection, to describe the spin of fermions forming Cooper pairs. Gauging implies that superconductors are inherently bosonic systems, yet they are endowed with a gravito-magnetic anomaly that is the remnant of their fermionic origin. We recognize that this anomaly is related to the Gaiotto-Kapustin-Thorngren bosonization, achieved via gauging fermion parity $(-1)^F$, now included in the gauge dynamics. This anomaly characterizes gauged electronic matter in great generality in three and four spacetime dimensions, forbidding trivial massive phases at low energy. It holds beyond the validity of the Higgs model, nd in other kinds of superconductors as well. It also appears in the nontrivial massless phase of three-dimensional electrodynamics, recently understood.