Interacting topological phases and modular invariance

Details Interacting topological phases and modular invariance Interacting topological phases and modular invariance

2012-02-20

arxiv.org/abs/1202.4484v1

Physics

Condensed Matter

Strongly Correlated Electrons

10 pages

Scientific paper

We discuss a (2+1) dimensional topological superconductor with $N_f$ left- and right-moving Majorana edge modes and a $\mathbb{Z}_2\times \mathbb{Z}_2$ 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 $N_f=8$ is unstable against interactions, and a $\mathbb{Z}_2\times \mathbb{Z}_2$ 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 non-chiral Majorana edge states is the physical manifestation of the bulk topological superconductors classified by $\mathbb{Z}_8$.

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