Scalar QED in AdS

TL;DR

This paper analyzes scalar QED in Anti-de Sitter space, computing the photon propagator exactly at large Nf and exploring boundary four-point functions and phase transitions, revealing IR divergences and boundary RG flows.

Contribution

It provides an exact photon propagator in AdS for scalar QED at large Nf and studies boundary correlators and phase structure, including IR effects and boundary RG flows.

Findings

Exact photon propagator in AdS at large Nf

Boundary four-point functions in Coulomb and Higgs phases

IR divergence induces boundary RG flow in D=3

Abstract

We consider scalar QED with $N_f$ flavors in AdS$_D$. 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 $N_f$. We then apply this result to compute the boundary four-point function of the charged operators at leading order in $1/N_f$ 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 $N_f$, 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.