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.

v1: 66 pages, 14 figures, 7 tables; v2: revtex-2 version, typos corrected

References in corpus (12)

• Properties of an algebraic spin liquid on the kagome lattice
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Algebraic spin liquid as the mother of many competing orders
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• On the Phase Structure of Many-Flavor QED${}_3$
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Critical behavior of the (2+1)-dimensional Thirring model
• Critical Flavor Number in the Three Dimensional Thirring Model
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• The Inversion Formula and 6j Symbol for 3d Fermions