## Abstract

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

Original language | English |
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Article number | 70 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2018 |

### Bibliographical note

Funding Information:We would like to thank John Cardy, Liam Fitzpatrick, Thomas Hartman, Matthew Head-rick, Tarun Grover, Mark Srednicki, Matthew Walters and Sasha Zhiboedov for valuable discussions. The research of NL is supported in part by funds provided by MIT-Skoltech Initiative. AD is supported by NSF grant PHY-1720374. This work is supported by the Office of High Energy Physics of U.S. Department of Energy under grant Contract Number DE-SC0012567.

Publisher Copyright:

© 2018, The Author(s).

## Keywords

- Conformal Field Theory
- Integrable Hierarchies
- Thermal Field Theory

## ASJC Scopus subject areas

- Nuclear and High Energy Physics