Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Interacting String Multi-verses and Holographic Instabilities of Massive Gravity

Elias Kiritsis, Vasilis Niarchos

TL;DR

This work develops a holographic framework in which products of large-N CFTs coupled by multi-trace interactions realize a quantum multi-gravity theory on unions of AdS spaces. One-loop effects induce a small graviton mass for a linear combination of gravitons, while the AdS/CFT perspective provides a controlled setting to examine classic massive gravity issues such as instabilities and strong coupling. The analysis combines conformal perturbation theory on the boundary with bulk implications, revealing a circle of perturbative fixed points with nonzero inter-CFT coupling under specific dimension conditions and showing that, at leading order, single-trace couplings remain unaltered. The results suggest that, with careful boundary-condition tuning, stable massive gravity is achievable in holographic contexts, with the UV behavior softened by bulk bound states and nonlocal stringy features, though generic backgrounds tend to erase graviton mass via backreaction. The work also bridges ideas of multi-verse versus multi-throat geometries and points to possible cosmological applications and deconstructions of gravitational dimensions through multiply coupled CFTs.

Abstract

Products of large-N conformal field theories coupled by multi-trace interactions in diverse dimensions are used to define quantum multi-gravity (multi-string theory) on a union of (asymptotically) AdS spaces. One-loop effects generate a small O(1/N) mass for some of the gravitons. The boundary gauge theory and the AdS/CFT correspondence are used as guiding principles to study and draw conclusions on some of the well known problems of massive gravity - classical instabilities and strong coupling effects. We find examples of stable multi-graviton theories where the usual strong coupling effects of the scalar mode of the graviton are suppressed. Our examples require a fine tuning of the boundary conditions in AdS. Without it, the spacetime background backreacts in order to erase the effects of the graviton mass.

Interacting String Multi-verses and Holographic Instabilities of Massive Gravity

TL;DR

This work develops a holographic framework in which products of large-N CFTs coupled by multi-trace interactions realize a quantum multi-gravity theory on unions of AdS spaces. One-loop effects induce a small graviton mass for a linear combination of gravitons, while the AdS/CFT perspective provides a controlled setting to examine classic massive gravity issues such as instabilities and strong coupling. The analysis combines conformal perturbation theory on the boundary with bulk implications, revealing a circle of perturbative fixed points with nonzero inter-CFT coupling under specific dimension conditions and showing that, at leading order, single-trace couplings remain unaltered. The results suggest that, with careful boundary-condition tuning, stable massive gravity is achievable in holographic contexts, with the UV behavior softened by bulk bound states and nonlocal stringy features, though generic backgrounds tend to erase graviton mass via backreaction. The work also bridges ideas of multi-verse versus multi-throat geometries and points to possible cosmological applications and deconstructions of gravitational dimensions through multiply coupled CFTs.

Abstract

Products of large-N conformal field theories coupled by multi-trace interactions in diverse dimensions are used to define quantum multi-gravity (multi-string theory) on a union of (asymptotically) AdS spaces. One-loop effects generate a small O(1/N) mass for some of the gravitons. The boundary gauge theory and the AdS/CFT correspondence are used as guiding principles to study and draw conclusions on some of the well known problems of massive gravity - classical instabilities and strong coupling effects. We find examples of stable multi-graviton theories where the usual strong coupling effects of the scalar mode of the graviton are suppressed. Our examples require a fine tuning of the boundary conditions in AdS. Without it, the spacetime background backreacts in order to erase the effects of the graviton mass.

Paper Structure

This paper contains 34 sections, 129 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Massive gravity -- motivation and problems
  3. Massive gravity in a holographic context -- an overview of the paper
  4. Large-$N$ theories and massive gravitons: estimating the cutoffs
  5. Estimates of the graviton masses
  6. The associated UV strong-coupling cutoffs
  7. Higher dimensional CFTs and multi-gravity in AdS spaces
  8. RG flows of multi-trace couplings in conformal perturbation theory
  9. Fixed points at leading order in $1/N$
  10. Fixed points at next-to-leading order in $1/N$
  11. Short summary
  12. Examples
  13. Multiply coupled CFTs
  14. Lessons for massive gravity
  15. The dual gravitational theory
  16. ...and 19 more sections

Figures (3)

  • Figure 1: A diagrammatic representation of the one-loop amplitude that gives a mass to a linear combination of two gravitons, each living on a different AdS space. The mixed boundary conditions for the dual scalars $\phi_1,\phi_2$ give a non-vanishing 1-2 graviton propagator.
  • Figure 2: A circle of fixed points of the one-loop $\beta$-function in the $(g_{11},g_{22},g_{12})$ plane for $a=\frac{d}{2}-\Delta_1=\Delta_2-\frac{d}{2}>0$. The $\beta$-function vector field vanishes on the fixed circle $C$ at the center of the plot, and at the special points $A=(\frac{a}{4},0,0)$ and $B=(0,-\frac{a}{4},0,0)$. Points on the fixed circle with $g_{12}\neq0$ and point $B$ are repellors of the RG flow, whereas point $A$ is an attractor.
  • Figure 3: A 2D slice of the RG flow vector field along the $g_{12}=0$ plane. Point $B$ is a repellor, $O$ and $O'$ are saddle points and point $A$ is an attractor.