Abstract
In the framework of the AdS3/ CFT2 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 AdS3. Both of the methods yield the same precise relation between the eigenvalues and the final black hole temperature at late Lorentzian time.
Highlights
Black holes and one expects to gain a lot of insight on the black hole information problem solely from the study of black hole physics in AdS31
Within the framework of the AdS3/ CFT2 correspondence, it would be tempting to create a heavy state in the CFT and understand under which conditions the late time behavior of the correlators evaluated on the state are indistinguishable to correlators on the thermal state dual to the black hole spacetime
We find that the mode u1(z) should be given by a solution that corresponds to a BTZ black hole, since this is the situation that the collapse process should converge to at late times
Summary
We shall setup our problem and introduce the computational tools we shall be using in the rest of the paper. First we shall present the configuration of a finite number of heavy operators that represents an arbitrarily heavy state Each of these heavy operator insertions is dual to adding a conical defect or a black hole in the bulk AdS3. We are interested in studying the final collapse states achieved through collisions among those defects or black holes at late Lorentzian time. This collapse is captured by measuring certain correlators of probe operators in the heavy background. The conformal block decomposition techniques in CFT2 simplifies computations of these correlation functions greatly. After presenting these techniques, the rest of the section will be devoted. To presenting the main technical obstacle that we would like to overcome in this paper, namely the “uniformization problem” in our setup
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