Conformality and self-duality of N = 2 QED3

We study the IR phase of three dimensional quantum electrodynamics (QED3) coupled to Nf=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×U(1)t)/Z2→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)→SU(2)f×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 Nf=2 QED3. 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 Nf=2 QED3 is not conformal.