Nonperturbative beta function in three-dimensional electrodynamics

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 conf c the system is in a conformal gapless state, while for small N < N χSB c the fermions are expected to develop a dynamical mass due to spontaneous chiral symmetry breaking. Using 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 conf 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. arXiv:1604.06354v3 [hep-th]

Section: Discussionsupporting

confidence: 92%

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

Janssen

2016

“…In this work, we determine the ratio f /T 3 in QED3 non-perturbatively for all (weak to strong) values of the dimensionless coupling e 2 N f T to NLO at large N f using well-established field theory techniques. Our results thus generalize studies of QED3 at T = 0 [12,13] to arbitrary temperature, and may be useful as a reference for lattice gauge theory studies [14][15][16][17][18][19], dualities found for "cousins" of QED in 2+1 dimensions [20][21][22], conformal QED3 studies [23,24], as well as condensed matter systems [25].…”

Section: Introductionsupporting

confidence: 71%

Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling

Romatschke

Säppi

2019

In 2+1 dimensions, QED becomes exactly solvable for all values of the fermion charge e in the limit of many fermions N f 1. We present results for the free energy density at finite temperature T to next-to-leading-order in large N f . In the naive large N f limit, we uncover an apparently UV-divergent contribution to the vacuum energy at order O( e 6 N 3 f ), which we argue to become a finite contribution of order O(e 6 N 4 f ) when resumming formally higher-order 1/N f contributions. We find the finite-temperature free energy to be well-behaved for all values of the dimensionless coupling e 2 N f /T , and to be bounded by the free energy of N f free fermions and non-interacting QED3, respectively. We invite follow-up studies from finite-temperature lattice gauge theory at large but fixed N f to test our results in the regime e 2 N f /T 1.

“…While these lattice models also contain monopole operators which can drastically modify the long-wavelength physics, for large enough N f these become irrelevant and the theory flows to a strongly coupled renormalization group fixed point. It is known that the large N f expansion breaks down below some critical value of N f , below which the theory is confining [54][55][56] [57].…”

Section: Introductionmentioning

confidence: 99%

Thermalization and chaos in QED3

Steinberg

Swingle

2019

We study the real time dynamics of N F flavors of fermions coupled to a U (1) gauge field in 2 + 1 dimensions to leading order in a 1/N F expansion. For large enough N F , this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in 1/N F . We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance. t ß t ß t ß (a) t ß t ß t ß (b)