Chern-Simons theory and Wilson loops in the Brillouin zone

Biao Lian, Cumrun Vafa, Farzan Vafa, Shou Cheng Zhang

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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 six-dimensional phase space, where the physical space defects play the role of topological D-branes.

Original languageEnglish (US)
Article number094512
JournalPhysical Review B
Issue number9
StatePublished - Mar 20 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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