A Study of Quantum Field Theories in AdS at Finite Coupling

TL;DR

This paper investigates large N quantum field theories in AdS space, deriving scattering amplitudes and boundary correlators, revealing resonance phenomena, symmetry breaking, and critical points, thus connecting bulk dynamics with boundary conformal theories.

Contribution

It introduces a spectral bootstrap method to compute AdS scattering amplitudes at finite coupling, linking bulk resonances and boundary conformal structures.

Findings

Derived AdS 4-particle scattering amplitude in terms of a spectral function.

Identified AdS analog of flat space resonances and symmetry-breaking phases.

Provided evidence for boundary conformal manifolds and critical points in the models.

Abstract

We study the $O(N)$ and Gross-Neveu models at large $N$ on AdS$_{d+1}$ background. Thanks to the isometries of AdS, the observables in these theories are constrained by the SO$(d,2)$ conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek, and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS $4$-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in $\frac{1}{N}$, and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic $O(N)$ model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS$_2$ evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.