title: Quantum Electrodynamics in d=3 from the ε Expansion.
abstract: We study quantum electrodynamics in d=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 fixed point in d=4-2ε 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=4-2ε that correspond to the additional conserved currents at d=3 and compute their infrared dimensions.
authors.affiliation: Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Di Pietro
authors.affiliation: Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel.
authors.forename: Zohar
authors.initials: Z
authors.lastname: Komargodski
authors.affiliation: Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel.
authors.forename: Itamar
authors.initials: I
authors.lastname: Shamir
authors.affiliation: Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel.
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Stamou