Conformal Field Theory, Geometry, and Entropy

Abstract

In the context of the AdS/CFT correspondence, an explicit relation between the physical degrees of freedom of 2+1d gravity and the stress tensor of 1+1d conformal field theory is exhibited. Gravity encodes thermodynamic state variables of conformal field theory, but does not distinguish among different CFT states with the same expectation value for the stress tensor. Simply put, gravity is thermodynamics; gauge theory is statistical mechanics.

16 pages, harvmac. v2: References corrected. v3: References corrected, discussion added regarding the relation between the classical Liouville solution and the Cardy formula

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