Conformality and self-duality of $N_f=2$ QED${}_3$

Abstract

We study the IR phase of three dimensional quantum electrodynamics (QED${}_3$) coupled to $N_f=2$ flavors of two-component Dirac fermions, which has been controversial for decades. This theory has been proposed to be self-dual with symmetry enhancement $(SU(2{)}_f\times U(1{)}_t)/{\mathbb{Z}}_2\to O(4)$ at the IR fixed point. We focus on the four-point correlator of monopole operators with unit topological charge of $U(1{)}_t$. We illustrate the $O(4)\to SU(2{)}_f\times U(1{)}_t$ branching rules based on an $O(4)$ symmetric positive structure in the monopole four-point crossing equations. We use conformal bootstrap method to derive nonperturbative constraints on the CFT data and test the conformality and self-duality of $N_f=2$ QED${}_3$. In particular we find the CFT data obtained from previous lattice simulations can be ruled out by introducing irrelevant assumptions in the spectrum, indicating the IR phase of $N_f=2$ QED${}_3$ is not conformal.

Comments: 4+5 pages, 2+1 figures; v2: references added, typos corrected; v3: 3+1 figures, explanation on the parity charges added, matches version to appear in PLB