Dual QED3 at "NF = 1/2" is an interacting CFT in the infrared

TL;DR

This paper demonstrates that dual QED3 with a single Dirac fermion flows to an interacting conformal field theory in the infrared, stabilized by gauge fluctuations and four-fermi interactions, relevant for topological insulator surfaces.

Contribution

It shows that dual QED3 at NF=1/2 is an interacting CFT stabilized by gauge and four-fermi interactions, with implications for fermion dualities and topological insulators.

Findings

Dual QED3 flows to an interacting CFT in the IR.

Gauge fluctuations stabilize the four-fermi coupling.

Constraints on topological current correlators from duality.

Abstract

We study the fate of weakly coupled dual QED3 in the infrared, that is, a single two-component Dirac fermion coupled to an emergent U(1) gauge field, but without Chern-Simons term. This theory has recently been proposed as a dual description of 2D surfaces of certain topological insulators. Using the renormalization group, we find that the interplay of gauge fluctuations with generated interactions in the four-fermi sector stabilizes an interacting conformal field theory (CFT) with finite four-fermi coupling in the infrared. The emergence of this CFT is due to cancellations in the $\beta$-function of the four-fermi coupling special to "NF = 1/2". We also quantify how a possible "strong" Dirac fermion duality between a free Dirac cone and dual QED3 would constrain the universal constants of the topological current correlator of the latter.