Bootstrapping <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> conformal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>QED</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
Soner Albayrak, Rajeev S. Erramilli, Zhijin Li, David Poland, Y. L. Xin
Abstract
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.