Conformal boundary conditions for a 4d scalar field

Abstract

We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED_33 with N_fNf flavors and a Chern-Simons term at level kk, in the large-N_fNf limit with fixed k/N_fk/Nf. We find that interacting boundary conditions only exist when k≠ 0k≠0. To obtain this result we compute the \betaβ functions of the classically marginal couplings at the first non-vanishing order in the large-N_fNf expansion, and to all orders in k/N_fk/Nf and in the couplings. To check vacuum stability we also compute the large-N_fNf effective potential. We compare our results with the the known conformal bootstrap bounds.