Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion

Abstract

We study the fixed point that controls the IR dynamics of QED in $d=4-2\epsilon$. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in $\epsilon$-expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to $d=3$ to estimate their value at the IR fixed point of QED${}_3$ as function of the number of fermions $N_f$. The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of $N_f$, which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, $\epsilon$-expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of $N_f$.

39 pages, 5 figures

References in corpus (12)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Algebraic spin liquid as the mother of many competing orders
• Conformal Bootstrap in Mellin Space
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• More Abelian Dualities in 2+1 Dimensions
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Generalized Wilson-Fisher critical points from the conformal OPE
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Erratum: algebraic spin liquid as the mother of many competing orders
• Chiral Symmetry breaking in Three Dimensional QED

Cited by in corpus (5)

• 3d Abelian Gauge Theories at the Boundary
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation