Towards Bootstrapping QED$_3$

TL;DR

This paper applies the conformal bootstrap method to study QED$_3$ with multiple fermion flavors, focusing on monopole operators to derive bounds on their scaling dimensions and identifying features near large N predictions.

Contribution

It introduces the bootstrap analysis of monopole operators in QED$_3$, providing new bounds and insights into the operator spectrum at finite N.

Findings

Bounds on monopole operator dimensions are established.

A kink in the bounds suggests a potential conformal phase.

Results align with large N extrapolations for N=4 and N=6.

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 $N=6$.