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.
