Chern-Simons Theory and Wilson Loops in the Brillouin Zone
  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. 
Biao Lian and Cumrun Vafa and Farzan Vafa and Shou-Cheng Zhang
cond-mat.mes-hall cond-mat.supr-con hep-th