### Abstract

In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical method requires a generalization of a formula due to by Hermann Weyl. While the first paper discussed the framework in Euclidean (Minkowski) space, here we discuss how this framework generalizes to spaces of constant sectional curvature. We focus primarily on anti de Sitter space. We then discuss how such a theory can give rise to a cosmological constant and Planck mass that are within reasonable bounds of the experimental values.

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

Article number | 33 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2017 |

### Fingerprint

### Keywords

- Effective field theories
- Large Extra Dimensions
- p-branes

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2017*(3), [33]. https://doi.org/10.1007/JHEP03(2017)033

**Emergent gravity in spaces of constant curvature.** / Alvarez, Orlando; Haddad, Matthew.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2017, no. 3, 33. https://doi.org/10.1007/JHEP03(2017)033

}

TY - JOUR

T1 - Emergent gravity in spaces of constant curvature

AU - Alvarez, Orlando

AU - Haddad, Matthew

PY - 2017/3/1

Y1 - 2017/3/1

N2 - In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical method requires a generalization of a formula due to by Hermann Weyl. While the first paper discussed the framework in Euclidean (Minkowski) space, here we discuss how this framework generalizes to spaces of constant sectional curvature. We focus primarily on anti de Sitter space. We then discuss how such a theory can give rise to a cosmological constant and Planck mass that are within reasonable bounds of the experimental values.

AB - In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical method requires a generalization of a formula due to by Hermann Weyl. While the first paper discussed the framework in Euclidean (Minkowski) space, here we discuss how this framework generalizes to spaces of constant sectional curvature. We focus primarily on anti de Sitter space. We then discuss how such a theory can give rise to a cosmological constant and Planck mass that are within reasonable bounds of the experimental values.

KW - Effective field theories

KW - Large Extra Dimensions

KW - p-branes

UR - http://www.scopus.com/inward/record.url?scp=85014969859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014969859&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2017)033

DO - 10.1007/JHEP03(2017)033

M3 - Article

AN - SCOPUS:85014969859

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 33

ER -