LAUSR

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here, the authors show that for three-dimensional (3D) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a momentum-space Chern-Simons gauge theory, which is the effective theory of the system. Furthermore, the gapless nodal lines in the momentum space which may arise in such superconductors play exactly the role of Wilson loop observables, and their linking and knot invariants modify the gravitational theta angle which can be evaluated from the Chern-Simons action. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. The authors also show how this idea may be potentially generalized to realize topological strings in six-dimensional phase space, where the physical space defects play the role of topological D-branes.