Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED

Abstract

The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N>N_c^{conf}$ the system is in a conformal gapless state, while for small $N<N_c^{\chi SB}$ the fermions are expected to develop a dynamical mass due to spontaneous chiral symmetry breaking. Using $\epsilon$ expansion near the lower critical dimension of 2, as well as the recent results on the generalization of the $F$ theorem to continuous dimension, we show that $N_c^{conf}>N_c^{\chi SB}$. There is therefore an intermediate range of values of $N$ at which a third phase is stabilized. We demonstrate that this phase is characterized by spontaneous breaking of Lorentz symmetry, in which a composite vector boson field acquires a vacuum expectation value with the fermions and the photon remaining massless.

7 pages, 3 figures, v2: presentation clarified and streamlined, flow diagrams added, references added, v3: additional comments and explanations, published version

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• Critical behavior of the QED${}_3$-Gross-Neveu-Yukawa model at four loops
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• Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge
• Deconfined criticality from the QED${}_3$-Gross-Neveu model at three loops
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Thermalization and chaos in QED${}_3$
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Effects of random potentials in three-dimensional quantum electrodynamics
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Critical properties of three-dimensional many-flavour QEDs
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• Critical number of fermions in three-dimensional QED
• Spontaneous symmetry breaking of $\mathrm{SO}(2N)$ in Gross--Neveu theory from $2+\epsilon$ expansion
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model