Bootstrapping $N_f=4$ conformal QED${}_3$

Abstract

We present the results of a conformal bootstrap study of the presumed unitary IR fixed point of quantum electrodynamics in three dimensions (QED${}_3$) coupled to $N_f=4$ two-component Dirac fermions. Specifically, we study the four-point correlators of the $SU(4)$ adjoint fermion bilinear $r$ and the monopole of lowest topological charge ${\mathcal{M}}_{1/2}$. Most notably, the scaling dimensions of the fermion bilinear $r$ and the monopole ${\mathcal{M}}_{1/2}$ are found to be constrained into a closed island with a combination of spectrum assumptions inspired by the $1/N_f$ perturbative results as well as a novel interval positivity constraint on the next-lowest-charge monopole ${\mathcal{M}}_1$. Bounds in this island on the $SU(4)$ and topological $U(1{)}_t$ conserved current central charges $c_J$, $c_J^t$, as well as on the stress tensor central charge $c_T$, are comfortably consistent with the perturbative results. Together with the scaling dimensions, this suggests that a part of estimates from the $1/N_f$ expansion -- even at $N_f=4$ -- provide a self-consistent solution to the bootstrap crossing relations, despite some of our assumptions not being strictly justified.

arXiv commentv1: 66 pages, 14 figures, 7 tables; v2: revtex-2 version, typos corrected

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