Abstract
We identify typical high energy eigenstates in two-dimensional conformal field theories at finite c and establish that correlation functions of the stress tensor in such states are accurately thermal as defined by the standard canonical ensemble. Typical states of dimension h are shown to be typical level h/c descendants. In the AdS3/CFT2 correspondence, it is such states that should be compared to black holes in the bulk. We also discuss the discrepancy between thermal correlators and those computed in high energy primary states: the latter are reproduced instead by a generalized Gibbs ensemble with extreme values chosen for the chemical potentials conjugate to the KdV charges.
Highlights
We focus here on universal aspects of this question
We identify typical high energy eigenstates in two-dimensional conformal field theories at finite c and establish that correlation functions of the stress tensor in such states are accurately thermal as defined by the standard canonical ensemble
We discuss the discrepancy between thermal correlators and those computed in high energy primary states: the latter are reproduced instead by a generalized Gibbs ensemble with extreme values chosen for the chemical potentials conjugate to the KdV charges
Summary
We write the corresponding torus 2-point function as J(w1)J(w2) L,β. This, along with the modular property, determines the 2-point function up to a position independent constant. The constant is determined in terms of the generalized partition function with a chemical potential, Z(q, y). ], where denotes the charge corresponding to the current J. This structure arises from Ward identities, and explicit formulas are provided in [21]. We will use this free boson result in the following, keeping in mind that the general correlator just differs from this by a position independent constant. It will be useful to reexpress the correlator as a mode sum in the free boson theory. The equivalence of (2.5) and (2.13) is shown in appendix A.1
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