Towards bootstrapping QED₃

Abstract: We initiate the conformal bootstrap study of Quantum Electrodynamics in 2+1 space-time dimensions (QED₃) with N flavors of charged fermions by focusing on the 4-point function of four monopole operators with the lowest unit of topological charge. We obtain upper bounds on the scaling dimension of the doubly-charged monopole operator, with and without assuming other gaps in the operator spectrum. Intriguingly, we find a (gap-dependent) kink in these bounds that comes reasonably close to the large N extrapolation of the scaling dimensions of the singly-charged and doubly-charged monopole operators down to N = 4 and N = 6.