Holographic boundary actions in AdS3/CFT2 revisited

The generating functional of stress tensor correlation functions in two-dimensional conformal field theory is the nonlocal Polyakov action, or equivalently, the Liouville or Alekseev-Shatashvili action. I review its holographic derivation within the AdS(3)/CFT2 correspondence, both in metric and Chern-Simons formulations. I also provide a detailed comparison with the well-known Hamiltonian reduction of three-dimensional gravity to a flat Liouville theory, and conclude that the two results are unrelated. In particular, the flat Liouville action is still off-shell with respect to bulk equations of motion, and simply vanishes in case the latter are imposed. The present study also suggests an interesting re-interpretation of the computation of black hole spectral statistics recently performed by Cotler and Jensen as that of an explicit averaging of the partition function over the boundary source geometry, thereby providing potential justification for its agreement with the predictions of a random matrix ensemble.

Automated summary

The study examines the generating functional of stress tensor correlation functions in two-dimensional conformal field theory, reviewing the holographic derivation within the AdS(3)/CFT2 correspondence and comparing it with the Hamiltonian reduction of three-dimensional gravity to a flat Liouville theory. It also discusses the re-interpretation of the computation of black hole spectral statistics as an explicit averaging of the partition function over the boundary source geometry.