Gauge interactions and topological phases of matter

TL;DR

This work investigates how strongly coupled gauge dynamics influence 3+1D CP-protected SPT phases. It develops a general criterion for when gauging a simple, connected, simply connected group with zero effective theta angle preserves the original SPT phase, and shows that infrared Goldstone dynamics can reproduce ultraviolet topological data via the $\,\eta$ invariant. Using a nonperturbative SUSY setup based on ${\cal N}=2$ $SU(2)$ gauge theory with $N_f=4$ and its S-dual description, the authors explicitly realize a continuous deformation that connects the ν=16 phase of Majorana fermions to the trivial ν=0 phase, thereby illustrating the collapse of the free fermion classification from $\mathbb{Z}$ to $\mathbb{Z}_{16}$. The results highlight interfaces between high-energy gauge dynamics, cobordism-type invariants, and condensed-matter SPT physics, and suggest broader applicability to boundary theories and other dualities.

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 $ν{=}16$ phase of Majorana fermions can be continuously connected to the trivial $ν{=}0$ phase.

Figures (2)

• Figure 1: On the electric side, the point $C$ is where the four quarks become massless, while the point $A$ and $B$ are the points where a monopole and a dyon become massless, respectively. On the magnetic side, the point $A$ is where a dual quark becomes massless, the point $B$ is where the dyon becomes massless, and the point $C$ is where four monopoles become massless. The $\mathsf{CP}$ acts by sending $u\to \overline u$. In particular, the points $A$, $B$ and $C$ preserve $\mathsf{CP}$ and are on the real axis.
• Figure 2: The overall picture. In the electric theory, the Higgs phase and the confined phase can be smoothly connected as we discussed in Sec. \ref{['subsec:general']}. The confined phase of the electric theory is dual to the Higgs phase of the magnetic theory. When the theory is Higgsed, we can perform weakly coupled analysis. In the Higgs phase of the electric theory, we get $\nu=16$ when we change the mass $m$ from positive to negative as argued in Sec. \ref{['subsec:general']}. In Sec. \ref{['subsec:continuous']}, we are going to show that the Higgs phase of the magnetic theory has $\nu=0$.