Multitrace deformations, Gamow states, and Stability of AdS/CFT

TL;DR

This paper explores how multitrace deformations in large N conformal field theories influence their gravity duals, revealing resonant behaviors linked to stability and Nambu-Goldstone modes in AdS/CFT.

Contribution

It provides a detailed mapping of multitrace deformations to boundary terms in gravity and analyzes the resulting RG flows and resonant states, including stability conditions.

Findings

Doubletrace deformations induce RG flows between fixed points.

Resonant behavior corresponds to Gamow states in gravity dual.

Stability theorem established for scalar/gravity systems with boundary potentials.

Abstract

We analyze the effect of multitrace deformations in conformal field theories at leading order in a large N approximation. These theories admit a description in terms of a weakly coupled gravity dual. We show how the deformations can be mapped into boundary terms of the gravity theory and how to reproduce the RG equations found in field theory. In the case of doubletrace deformations, and for bulk scalars with masses in the range $-d^2/4<m^2<-d^2/4+1$, the deformed theory flows between two fixed points of the renormalization group, manifesting a resonant behavior at the scale characterizing the transition between the two CFT's. On the gravity side the resonance is mapped into an IR non-normalizable mode (Gamow state) whose overlap with the UV region increases as the dual operator approaches the free field limit. We argue that this resonant behavior is a generic property of large N theories in the conformal window, and associate it to a remnant of the Nambu-Goldstone mode of dilatation invariance. We emphasize the role of nonminimal couplings to gravity and establish a stability theorem for scalar/gravity systems with AdS boundary conditions in the presence of arbitrary boundary potentials and nonminimal coupling.