Spontaneous breaking of Lorentz symmetry in (2+1)-dimensional QED

The phase diagram of 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 the system is in a conformal state with anomalous exponents, while for small N < N c the fermions are expected to develop a dynamical mass due to spontaneous chiral symmetry breaking. Using expansion near the lower critical dimension of two, in combination with the recent results on the generalization of the F theorem to continuous dimension, we show that N c > N χSB c . 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.