Axion field theory approach and the classification of interacting topological superconductors

Abstract

In this paper, we discuss the topological classification of time-reversal invariant topological superconductors. Based on the axion field theory developed in a previous work (Phys. Rev. B $87$ 134519 (2013)), we show how a simple quantum anomaly in vortex-crossing process predicts a ${\mathbb{Z}}_{16}$ classification of interacting topological superconductors, in consistency with other approaches. We also provide a general definition of the quantum anomaly and a general geometric argument that explains the ${\mathbb{Z}}_{16}$ on more general grounds. Furthermore, we generalize our approach to all $4n$ dimensions (with $n$ an integer), and compare our results with other approaches to the topological classification.

16 pages (9 pages main text and 7 pages appendices), 15 figures

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