Vacuum block thermalization in semi-classical 2d CFT

TL;DR

This paper investigates the conditions under which states in large central charge 2d CFTs thermalize, linking Virasoro coadjoint orbits to stability intervals of Hill's equation, and provides criteria for thermalization.

Contribution

It establishes a novel connection between Virasoro coadjoint orbits and Hill's equation stability, offering new criteria for thermalization in 2d CFTs.

Findings

States failing to thermalize can be turned into thermalizing states by increasing energy.

Lower bounds for threshold energy are derived as criteria for thermalization.

The work links gravitational collapse in AdS3 to CFT state stability.

Abstract

The universal nature of black hole collapse in asymptotically $AdS_3$ gravitational theories suggests that its holographic dual process, thermalization, should similarly be fixed by the universal features of 2d CFT with large central charge $c$. It is known that non-equilibrium states with scaling dimensions of order $c$ can be sorted into states that eventually thermalize and those that fail to do so. By proving an equivalence between bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill's equation it is shown that a state that fails to thermalize can be promoted to a thermalizing state by preparing the system beforehand with an energy greater than an appropriate threshold energy. It is generally a difficult problem to ascertain whether a state will thermalize or not. As partial progress to this problem a set of lower bounds are presented for the treshold energy, which can alternatively be interpreted as criteria for thermalization.