### Abstract

We review boundary rigidity theorems assessing that, under appropriate conditions, riemannian manifolds with the same spectrum of boundary geodesies are isometric. We show how to apply these theorems to the problem of reconstructing a d + 1 dimensional, negative curvature space-time from boundary data associated to two-point functions of high-dimension local operators in a conformal field theory. We also show simple, physically relevant examples of negative-curvature spaces that fail to satisfy in a subtle way some of the assumptions of rigidity theorems. In those examples, we explicitly show that the spectrum of boundary geodesics is not sufficient to reconstruct the metric in the bulk. We also survey other reconstruction procedures and comment on their possible implementation in the context of the holographic AdS/CFT duality.

Original language | English (US) |
---|---|

Pages (from-to) | 899-922 |

Number of pages | 24 |

Journal | Journal of High Energy Physics |

Volume | 8 |

Issue number | 1 |

State | Published - Jan 1 2004 |

### Fingerprint

### Keywords

- AdS-CFT and dS-CFT Correspondence
- Black Holes

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*8*(1), 899-922.

**Boundary rigidity and holography.** / Porrati, Massimo; Rabadan, Raul.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 8, no. 1, pp. 899-922.

}

TY - JOUR

T1 - Boundary rigidity and holography

AU - Porrati, Massimo

AU - Rabadan, Raul

PY - 2004/1/1

Y1 - 2004/1/1

N2 - We review boundary rigidity theorems assessing that, under appropriate conditions, riemannian manifolds with the same spectrum of boundary geodesies are isometric. We show how to apply these theorems to the problem of reconstructing a d + 1 dimensional, negative curvature space-time from boundary data associated to two-point functions of high-dimension local operators in a conformal field theory. We also show simple, physically relevant examples of negative-curvature spaces that fail to satisfy in a subtle way some of the assumptions of rigidity theorems. In those examples, we explicitly show that the spectrum of boundary geodesics is not sufficient to reconstruct the metric in the bulk. We also survey other reconstruction procedures and comment on their possible implementation in the context of the holographic AdS/CFT duality.

AB - We review boundary rigidity theorems assessing that, under appropriate conditions, riemannian manifolds with the same spectrum of boundary geodesies are isometric. We show how to apply these theorems to the problem of reconstructing a d + 1 dimensional, negative curvature space-time from boundary data associated to two-point functions of high-dimension local operators in a conformal field theory. We also show simple, physically relevant examples of negative-curvature spaces that fail to satisfy in a subtle way some of the assumptions of rigidity theorems. In those examples, we explicitly show that the spectrum of boundary geodesics is not sufficient to reconstruct the metric in the bulk. We also survey other reconstruction procedures and comment on their possible implementation in the context of the holographic AdS/CFT duality.

KW - AdS-CFT and dS-CFT Correspondence

KW - Black Holes

UR - http://www.scopus.com/inward/record.url?scp=23144460175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23144460175&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23144460175

VL - 8

SP - 899

EP - 922

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

ER -