Bootstrapping Nf=4 conformal QED3

Le résumé fourni par la source

We present the results of a conformal bootstrap study of the presumed unitary IR fixed point of quantum electrodynamics in three dimensions (${\mathrm{QED}}_{3}$) 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 equations, despite some of our assumptions not being strictly justified.

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