Towards Bootstrapping QED${}_3$

Abstract

We initiate the conformal bootstrap study of Quantum Electrodynamics in $2+1$ space-time dimensions (QED${}_3$) 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 $N=6$.

29 pages plus an appendix, 5 figures, v2 minor improvements, refs added

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