Axion field theory approach and the classification of interacting topological superconductors

TL;DR

This paper uses axion field theory and quantum anomalies to classify interacting topological superconductors, revealing a $6$ classification in 3D and extending the approach to higher dimensions, aligning with other methods.

Contribution

It introduces a novel axion field theory framework and quantum anomaly analysis to classify topological superconductors, generalizing to all 4n dimensions and confirming the 6 classification.

Findings

Predicts 6 classification for 3D topological superconductors

Provides a geometric and anomaly-based classification framework

Extends classification approach to all 4n dimensions

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 ${\bf 87}$ 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.