Multi-Trace Operators and the Generalized AdS/CFT Prescription

TL;DR

This paper extends the AdS/CFT correspondence to include multi-trace interactions through generalized boundary conditions and a modified Legendre transform, exploring their effects on bulk quantization and boundary perturbations.

Contribution

It introduces a consistent formulation for incorporating double-trace perturbations into AdS/CFT, analyzing various coupling scenarios and deriving new boundary conditions and surface terms.

Findings

Double-trace perturbations allow irregular modes to propagate.

A new constraint ensures consistency across different scenarios.

Extension of Gibbons-Hawking term for non-minimal couplings.

Abstract

We show that multi-trace interactions can be consistently incorporated into an extended AdS/CFT prescription involving the inclusion of generalized boundary conditions and a modified Legendre transform prescription. We find new and consistent results by considering a self-contained formulation which relates the quantization of the bulk theory to the AdS/CFT correspondence and the perturbation at the boundary by double-trace interactions. We show that there exist particular double-trace perturbations for which irregular modes are allowed to propagate as well as the regular ones. We perform a detailed analysis of many different possible situations, for both minimally and non-minimally coupled cases. In all situations, we make use of a new constraint which is found by requiring consistence. In the particular non-minimally coupled case, the natural extension of the Gibbons-Hawking surface term is generated.