Gauge interactions and topological phases of matter

Abstract

We initiate the study of the effects of strongly-coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang-Mills field to preserve the topological phase of matter, and then show how the massless pions capture in the infrared the topological properties of the fermions in the ultraviolet. Finally, we use the S-duality of $\mathcal{N}=2$ supersymmetric $SU(2)$ gauge theory with $N_f=4$ flavors to show that the $\nu =16$ phase of Majorana fermions can be continuously connected to the trivial $\nu =0$ phase.

60 pages, 3 figures, v2:references added

References in corpus (5)

• Classification of topological insulators and superconductors in three spatial dimensions
• Generalized Global Symmetries
• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets
• Topological Number of Edge States
• Gapped Boundary Phases of Topological Insulators via Weak Coupling

Cited by in corpus (3)

• Comments on Symmetric Mass Generation in 2d and 4d
• More on time-reversal anomaly of 2+1d topological phases
• Understanding the index theorems with massive fermions