Chern-Simons Theory and Wilson Loops in the Brillouin Zone

TL;DR

This paper reveals that in 3D time-reversal invariant superconductors, the Berry connection acts as a Chern-Simons gauge field, linking topological invariants with observable physical effects like gravitomagnetoelectric phenomena.

Contribution

It introduces a novel interpretation of Berry connection as a Chern-Simons gauge field and connects nodal lines to Wilson loops and topological invariants in superconductors.

Findings

Nodal lines act as Wilson loops in the gauge theory.

Linking of nodal lines affects the gravitational theta angle.

Temperature gradients induce a gravitomagnetoelectric effect.

Abstract

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the 6 dimensional phase space, where the physical space defects play the role of topological D-branes.