On the universality of late-time correlators in semi-classical 2d CFTs

In the framework of AdS$_3$/ CFT$_2$ correspondence, we present a systematic analysis of the late time thermalization of a two dimensional CFT state created by insertion of small number of heavy operators on the vacuum. We show that at late Lorentzian time, the universal features of this thermalization are solely captured by the eigenvalues of the monodromy matrix corresponding to the solutions of the uniformization equation. We discuss two different ways to extract the monodromy eigenvalues while bypassing the need for finding explicitly the full monodromy matrix - first, using a monodromy preserving diffeomorphism and second using Chen-Simons formulation of gravity in AdS$_3$. Both of the methods yield the same precise relation between the eigenvalues and the final black hole temperature at late Lorentzian time.