Abstract
We construct black hole geometries in AdS3 with non-trivial values of KdV charges. The black holes are holographically dual to quantum KdV Generalized Gibbs Ensemble in 2d CFT. They satisfy thermodynamic identity and thus are saddle point configurations of the Euclidean gravity path integral. We discuss holographic calculation of the KdV generalized partition function and show that for a certain value of chemical potentials new geometries, not the conventional BTZ ones, are the leading saddles.
Highlights
2d CFT state carries non-trivial qKdV charges, local physics at late times was argued to be given by the KdV GGE state [13], ρGGE = e− k μkQ2k+1 /Z
In the previous works on the subject, both on holographic and the CFT sides [14,15,16,17], it was implicitly assumed that the BTZ black holes, i.e. eigenstates of Q1 = L0 − c/24 on the CFT side, are the leading saddle point configurations contributing to the KdV generalized partition function (1.2)
Conventional BTZ geometries emerge as a particular case, which is dual to the conventional Gibbs Ensemble, i.e. when all μ2k+1 = 0 except for μ1 = β
Summary
We provide mathematical preliminaries necessary for the general discussion of the consecutive sections. We aimed at a self-contained but concise presentation and many details and proofs were omitted. The reader is advised to consult the original papers by Witten, Novikov, and others [18,19,20,21,22] for a systematic presentation of the geometry of the co-adjoint orbits of Virasoro algebra, finite-zone solutions of the generalized KdV equations, and other related questions
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