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

TL;DR

This paper explores the phase diagram of massless QED in (2+ε) dimensions, revealing a new phase with spontaneous Lorentz symmetry breaking between the conformal and chiral symmetry breaking phases.

Contribution

It demonstrates the existence of an intermediate phase with spontaneous Lorentz symmetry breaking in (2+ε)-dimensional QED, extending understanding of phase transitions in quantum field theories.

Findings

N_c^{conf} > N_c^{ ext{χSB}}

Existence of an intermediate phase with Lorentz symmetry breaking

Composite vector boson acquires vacuum expectation value

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.