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AdS/CFT and gravity

Steven S. Gubser

TL;DR

The paper investigates how four-dimensional gravity and cosmology emerge from the AdS/CFT framework by treating a cutoff Planck brane in an AdS5 background as coupling gravity to a conformal field theory. It shows that a radiation-dominated FRW universe arises from an AdS–Schwarzschild bulk, with the Hawking temperature encoding the CFT temperature and a holographic derivation yielding G4 = 2 G5/L. A generalized AdS/CFT prescription for Green's functions is developed, linking the boundary CFT dynamics to nonlocal corrections to gravity and to Newtonian deviations via the CFT stress-tensor correlator. The work then derives bounds on the AdS curvature scale L from gravitational experiments and string-theory considerations, finding L ≲ 1 nm for a GeV-scale string and stricter limits for higher scales, thus constraining observable deviations while confirming the consistency of gravity as emergent from a strongly coupled CFT in this setup.

Abstract

The radiation-dominated k=0 FRW cosmology emerges as the induced metric on a codimension one hypersurface of constant extrinsic curvature in the five-dimensional AdS-Schwarzschild solution. That we should get FRW cosmology in this way is an expected result from AdS/CFT in light of recent comments regarding the coupling of gravity to "boundary" conformal field theories. I remark on how this calculation bears on the understanding of Randall and Sundrum's "alternative to compactification." A generalization of the AdS/CFT prescription for computing Green's functions is suggested, and it is shown how gravity emerges from it with a strength G_4 = 2 G_5/L. Some numerical bounds are set on the radius of curvature L of AdS_5. One of them comes from estimating the rate of leakage of visible sector energy into the CFT. That rate is connected via a unitarity relation to deviations from Newton's force law at short distances. The best bound on L obtained in this paper comes from a match to the parameters of string theory. It is L < 1 nm if the string scale is 1 GeV. Higher string scales imply a tighter bound on L.

AdS/CFT and gravity

TL;DR

The paper investigates how four-dimensional gravity and cosmology emerge from the AdS/CFT framework by treating a cutoff Planck brane in an AdS5 background as coupling gravity to a conformal field theory. It shows that a radiation-dominated FRW universe arises from an AdS–Schwarzschild bulk, with the Hawking temperature encoding the CFT temperature and a holographic derivation yielding G4 = 2 G5/L. A generalized AdS/CFT prescription for Green's functions is developed, linking the boundary CFT dynamics to nonlocal corrections to gravity and to Newtonian deviations via the CFT stress-tensor correlator. The work then derives bounds on the AdS curvature scale L from gravitational experiments and string-theory considerations, finding L ≲ 1 nm for a GeV-scale string and stricter limits for higher scales, thus constraining observable deviations while confirming the consistency of gravity as emergent from a strongly coupled CFT in this setup.

Abstract

The radiation-dominated k=0 FRW cosmology emerges as the induced metric on a codimension one hypersurface of constant extrinsic curvature in the five-dimensional AdS-Schwarzschild solution. That we should get FRW cosmology in this way is an expected result from AdS/CFT in light of recent comments regarding the coupling of gravity to "boundary" conformal field theories. I remark on how this calculation bears on the understanding of Randall and Sundrum's "alternative to compactification." A generalization of the AdS/CFT prescription for computing Green's functions is suggested, and it is shown how gravity emerges from it with a strength G_4 = 2 G_5/L. Some numerical bounds are set on the radius of curvature L of AdS_5. One of them comes from estimating the rate of leakage of visible sector energy into the CFT. That rate is connected via a unitarity relation to deviations from Newton's force law at short distances. The best bound on L obtained in this paper comes from a match to the parameters of string theory. It is L < 1 nm if the string scale is 1 GeV. Higher string scales imply a tighter bound on L.

Paper Structure

This paper contains 5 sections, 44 equations, 2 figures.

Table of Contents

  1. Introduction
  2. A cosmological solution
  3. The general framework
  4. Bounds and estimates
  5. Discussion

Figures (2)

  • Figure 1: Contributions to the graviton propagator, following WittenComment: a) free graviton propagation; b) leading CFT correction. The blob between the stress tensor insertions is intended to denote the full $\langle TT \rangle_{\rm CFT}$ correlator.
  • Figure 2: a) Standard Model particles losing energy via graviton exchange to CFT excitations. b) The inclusive rate is given by a unitarity cut of the first correction to the graviton propagator.