On the Phase Structure of Many-Flavor QED${}_3$

Abstract

We analyze the many-flavor phase diagram of quantum electrodynamics (QED) in 2+1 (Euclidean) space-time dimensions. We compute the critical flavor number above which the theory is in the quasi-conformal massless phase. For this, we study the renormalization group fixed-point structure in the space of gauge interactions and pointlike fermionic self-interactions, the latter of which are induced dynamically by fermion-photon interactions. We find that a reliable estimate of the critical flavor number crucially relies on a careful treatment of the Fierz ambiguity in the fermionic sector. Using a Fierz-complete basis, our results indicate that the phase transition towards a chirally-broken phase occurring at small flavor numbers could be separated from the quasi-conformal phase at larger flavor numbers, allowing for an intermediate phase which is dominated by fluctuations in a vector channel. If these interactions approach criticality, the intermediate phase could be characterized by a Lorentz-breaking vector condensate.

19 pages, 8 figures, 2 tables

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• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge
• Thermalization and chaos in QED${}_3$
• Non-perturbative beta function in three-dimensional electrodynamics
• Momentum dependence of quantum critical Dirac systems
• Universal behavior of coupled order parameters below three dimensions
• Phase of the fermion determinant in QED_3 using a gauge invariant lattice regularization
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Infrared behavior of dynamical fermion mass generation in QED${}_3$
• Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model
• Renormalization of fermion velocity in finite temperature QED_{3}
• Critical properties of three-dimensional many-flavour QEDs
• Stability of $SU(N_c)$ QCD3 from the $\epsilon$-Expansion
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Critical number of fermions in three-dimensional QED