Dressing in AdS and a Conformal Bethe-Salpeter Equation

TL;DR

This paper develops a framework for Dyson equations in AdS space, revealing how dressing propagators affects CFT data, and introduces a conformal Bethe-Salpeter equation to describe bound states with quantum corrections.

Contribution

It introduces a novel approach to Dyson equations in AdS, linking them to large-N CFT corrections and deriving a conformal Bethe-Salpeter equation for bound states.

Findings

Dressed AdS propagators exhibit wavefunction renormalization and operator mixing.

Resummation of 1/N effects in CFT is derived from AdS dressing.

Bound states with conformal dimensions and binding energies are characterized.

Abstract

We initiate the study of Dyson equations of perturbative QFT in AdS and their consequences for large-N CFT. We show that the dressed one-particle AdS propagator features wavefunction renormalization and operator mixing, giving rise to finite corrections to OPE data. We show how the resummation of 1/N effects in the CFT emerges from the dressing in AdS. When a boundary-to-bulk propagator is dressed by propagators whose sum of conformal dimensions is lower than the main dimension, it cannot map onto a CFT source; we relate this to an AdS/CFT version of particle instability. We investigate the dressing of the two-particle propagator and obtain a conformal Bethe-Salpeter equation for the conformal partial wave of a "bound state" operator. We provide a self-contained calculation for the case of a ladder kernel. We show that a bound state with conformal dimension equal to the sum of its constituents plus a 1/N^2-suppressed "binding energy" emerges. Resummation of the Dyson equations is essential for deriving these results.