Interacting topological phases and modular invariance

Shinsei Ryu, Shou Cheng Zhang

Research output: Contribution to journalArticlepeer-review

164 Scopus citations


We discuss (2+1)-dimensional topological superconductors with N f left- and right-moving Majorana edge modes and a Z 2×Z 2 symmetry. In the absence of interactions, these phases are distinguished by an integral topological invariant N f. With interactions, the edge state in the case of N f=8 is unstable against interactions, and a Z 2×Z 2 invariant mass gap can be generated dynamically. We show that this phenomenon is closely related to the modular invariance of type II superstring theory. More generally, we show that the global gravitational anomaly of the nonchiral Majorana edge states is the physical manifestation of the bulk topological superconductors classified by Z 8.

Original languageEnglish (US)
Article number245132
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number24
StatePublished - Jun 27 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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