We consider scalar QED with Nfβ flavors in AdSDβ. For D<4 the theory is
strongly-coupled in the IR. We use the spin 1 spectral representation to
compute and efficiently resum the bubble diagram in AdS, in order to obtain the
exact propagator of the photon at large Nfβ. We then apply this result to
compute the boundary four-point function of the charged operators at leading
order in 1/Nfβ and exactly in the coupling, both in the Coulomb and in the
Higgs phase. In the first case a conserved current is exchanged in the
four-point function, while in the second case the current is absent and there
is a pattern of double-trace scaling dimension analogous to a resonance in flat
space. We also consider the BCFT data associated to the critical point with
bulk conformal symmetry separating the two phases. Both in ordinary
perturbation theory and at large Nfβ, in integer dimension D=3 an IR
divergence breaks the conformal symmetry on the boundary by inducing a boundary
RG flow in a current-current operator.Comment: 40 pages, 7 figure