## Abstract

In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in the large N limit, we discuss at non-linear-level the deduction of the zero mode effective Schwarzian action, featuring emergent finite reparametrization symmetry. We then discuss the question of identifying the bulk space-time of the SYK model. We explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions, leading to a dual theory with Euclidean AdS signature with additional leg-factors. We show that the SYK spectrum and the bi-local propagator can be obtained from a Horava-Witten type compactification of a three dimensional model.

Original language | English |
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Title of host publication | Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 - QTS-X/LT-XII, 2017 |

Editors | Vladimir Dobrev |

Pages | 43-61 |

Number of pages | 19 |

DOIs | |

State | Published - 2018 |

Event | International Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017 - Varna, Bulgaria Duration: Jun 19 2017 → Jun 25 2017 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 255 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | International Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017 |
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Country/Territory | Bulgaria |

City | Varna |

Period | 6/19/17 → 6/25/17 |

### Bibliographical note

Funding Information:Acknowledgements S.R.D. and A.J. thank the organizers of QTS10 for organizing a very stimulating meeting. We acknowledge helpful discussions with Robert de Melo Koch, Alexei Kitaev, Juan Maldacena, Gautam Mandal, Cheng Peng and Edward Witten on the topics of this work. We also thank Junggi Yoon for collaborations. This work of A.J. and K.S. are supported by the Department of Energy under contract DE-SC0010010. The work of KS is also supported by the Galkin Fellowship Award at Brown University. The work of S.R.D and A.G is partially supported by the National Science Foundation grant NSF-PHY-1521045.

Publisher Copyright:

© Springer Nature Singapore Pte Ltd. 2018.

## Keywords

- Collective field theory
- Holographic correspondence
- Large N expansion

## ASJC Scopus subject areas

- Mathematics (all)