Critical properties of three-dimensional many-flavour QEDs

TL;DR

This paper reviews various three-dimensional QED models with multiple flavors, analyzing their critical properties, phase structure, and mass generation through advanced computational methods in the large-$N_f$ limit.

Contribution

It provides the first comprehensive analysis of critical exponents and phase structure across multiple QED$_3$ variants using next-to-leading order $1/N_f$ expansion and dimensional regularization.

Findings

Critical exponents computed at next-to-leading order in $1/N_f$

Models flow to stable infra-red fixed points in the large-$N_f$ limit

Discussion of dynamical mass generation and phase transitions

Abstract

We review several variants of three-dimensional quantum electrodynamics (QED$_3$) with $N_f$ fermion (or boson) flavors including fermionic (or spinorial) QED$_3$, bosonic (or scalar) QED$_3$, $\mathcal{N}=1$ supersymmetric QED and also models of reduced QED (supersymmetric or not). We begin with an introduction to these models and their flow to a stable infra-red fixed point in the large-$N_f$ limit. We then present detailed state-of-the-art computations of the critical exponents of these models within the dimensional regularization (and reduction) scheme(s), at the next-to-leading order in the $1/N_f$ expansion and in an arbitrary covariant gauge. We finally discuss dynamical (matter) mass generation and the current status of our understanding of the phase structure of these models.