Critical properties of three-dimensional many-flavour QEDs

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.

LaTeX file with Tikz and feynMF package. 55 pages, 4 figures

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