## Abstract

Motivated by the Bekenstein-Hawking formula and the area law behaviour of entanglement entropy, we propose that in any UV finite theory of quantum gravity with a smooth spacetime, the total entropy for a pure state in a co-dimension one spatial region, to leading order, is given by S = _{4G}^{A}_{N}, where A is the area of the co-dimension two boundary. In the context of Dp brane holography we show that for some specially chosen regions bulk entanglement can be mapped to 'target space' entanglement in the boundary theory. Our conjecture then leads to a precise proposal for target space entanglement in the boundary theory at strong coupling and large N. In particular, it leads to the conclusion that the target space entanglement would scale like O(N^{2}) which is quite plausible in a system with O(N^{2}) degrees of freedom. Recent numerical advances in studying the D0 brane system hold out the hope that this proposal can be tested in a precise way in the future.

Original language | English |
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Article number | abafe4 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 53 |

Issue number | 44 |

DOIs | |

State | Published - Nov 2020 |

### Bibliographical note

Publisher Copyright:© 2020 IOP Publishing Ltd Printed in the UK

## Keywords

- Entanglement entropy
- Holography
- Matrix model

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- General Physics and Astronomy