Quantum Electrodynamics in d=3 from the epsilon-expansion

TL;DR

This paper uses epsilon-expansion techniques to analyze three-dimensional quantum electrodynamics (QED_3), identifying critical fermion flavors for phase transitions and exploring operator dimensions at the IR fixed point.

Contribution

It applies perturbative epsilon-expansion from four to three dimensions to study operator dimensions and symmetry enhancements in QED_3, estimating the critical number of fermion flavors.

Findings

Computed IR dimensions of fermion bilinear and quadrilinear operators.

Estimated the critical fermion number N_f^c for chiral symmetry breaking.

Identified operators corresponding to conserved currents and their dimensions.

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.