Revision 1

Accepted · first revision · record

Title: Critical flavor number for chiral symmetry breaking in QED3
Plain: Electrodynamics in two space dimensions with N species of massless electrons is scale invariant at long distances when N is large. Below which N this fails is unknown.
Precise: 3D QED with $N_{f}$ two-component Dirac fermions of unit charge ($N_{f}$ even, parity invariant) flows to an interacting CFT for large $N_{f}$. Determine $N_{f}^{c}$ such that for $N_{f} < N_{f}^{c}$ the IR breaks the $\mathrm{SU}(N_{f})$ flavor symmetry or is otherwise not conformal; in particular decide $N_{f} = 2$ and $N_{f} = 4$ (the latter describes the Dirac spin liquid).
Settled by: Conformal bootstrap islands or continuum-extrapolated lattice simulations that bracket $N_{f}^{c}$ and determine the fate of $N_{f}=2\text{ and }4$.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: contested
Status note: Estimates from Schwinger-Dyson equations, $\epsilon$ expansion, the F-theorem, lattice simulations and bootstrap disagree; recent lattice and bootstrap evidence favors conformality at $N_f = 4$.
Posed since: (empty)