Extended eigenstate thermalization and the role of FZZT branes in the Schwarzian theory

Pranjal Nayak (Department of Physics & Astronomy, University of Kentucky, 505 Rose St, Lexington, KY, U.S.A.) ; Julian Sonner (Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, Genève, 1211 Genève 4, Switzerland) ; Manuel Vielma (Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, Genève, 1211 Genève 4, Switzerland)

In this paper we provide a universal description of the behavior of the basic operators of the Schwarzian theory in pure states. When the pure states are energy eigenstates, expectation values of non-extensive operators are thermal. On the other hand, in coherent pure states, these same operators can exhibit ergodic or non-ergodic behavior, which is characterized by elliptic, parabolic or hyperbolic monodromy of an auxiliary equation; or equivalently, which coadjoint Virasoro orbit the state lies on. These results allow us to establish an extended version of the eigenstate thermalization hypothesis (ETH) in theories with a Schwarzian sector. We also elucidate the role of FZZT-type boundary conditions in the Schwarzian theory, shedding light on the physics of microstates associated with ZZ branes and FZZT branes in low dimensional holography.

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Published on:
27 March 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 3
Pages 1-40
DOI:
https://doi.org/10.1007/JHEP03(2020)168
arXiv:
1907.10061
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: