### Abstract

In this summary of my talk at Strings 2016, I explain how classical dynamics on an infinite tree graph can be dual to a conformal field theory defined over the p-adic numbers. An informal introduction to p-adic numbers is followed by a presentation of results on holographic three- and four-point functions. The simplicity of p-adic field theories and their similarity to ordinary field theories are illustrated through comparisons of holographic correlators and computations of simple loop diagrams on the field theory side. I close with a discussion of challenges and directions for future work.

Original language | English (US) |
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Pages (from-to) | 1655-1678 |

Number of pages | 24 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 21 |

Issue number | 7 |

DOIs | |

State | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)

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## Cite this

Gubser, S. S. (2017). A p-adic version of AdS/CFT.

*Advances in Theoretical and Mathematical Physics*,*21*(7), 1655-1678. https://doi.org/10.4310/ATMP.2017.v21.n7.a3