Quantum Electrodynamics in d=3 from the epsilon-expansion
Lorenzo Di Pietro, Zohar Komargodski, Itamar Shamir, Emmanuel Stamou
TL;DR
By perturbing QED_3 with $N_f$ flavors around $d=4-2\epsilon$, the paper identifies an IR fixed point at small $\epsilon$ and uses it to infer a three-dimensional conformal phase for sufficiently large $N_f$. It computes leading-order IR dimensions of fermion bilinears and SU(2N_f)-invariant quadrilinear operators, showing a quadrilinear can become relevant when $N_f$ is small, which yields the bound $N_f^c \le 2$ at leading order. The analysis reveals an enhanced $SU(2N_f)$ symmetry in $d=3$ and associates extra conserved currents $J^s_\mu$ and $K_{\mu\nu}$ with IR dimension 2, consistent with the 3d CFT currents. The work connects UV and IR theories, aligns with lattice and $F$-theorem expectations, and points to higher-order $\epsilon$ calculations and additional observables such as the stress tensor and sphere free energy for further validation.
Abstract
We study Quantum Electrodynamics in d=3 (QED_3) coupled to N_f flavors of fermions. The theory flows to an IR fixed point for N_f larger than some critical number N_f^c. For N_f<= N_f^c, chiral-symmetry breaking is believed to take place. In analogy with the Wilson-Fisher description of the critical O(N) models in d=3, we make use of the existence of a perturbative fixed point in d=4-2epsilon to study the three-dimensional conformal theory. We compute in perturbation theory the IR dimensions of fermion bilinear and quadrilinear operators. For small N_f, a quadrilinear operator can become relevant in the IR and destabilize the fixed point. Therefore, the epsilon-expansion can be used to estimate N_f^c. An interesting novelty compared to the O(N) models is that the theory in d=3 has an enhanced symmetry due to the structure of 3d spinors. We identify the operators in d=4-2epsilon that correspond to the additional conserved currents at d=3 and compute their infrared dimensions.