Conformal Field Theory, Geometry, and Entropy

TL;DR

This paper explores the relationship between 2+1d gravity and 1+1d conformal field theory within the AdS/CFT framework, highlighting how gravity encodes thermodynamic properties but not detailed microstates.

Contribution

It explicitly relates gravitational degrees of freedom to the stress tensor of the conformal field theory, emphasizing gravity's role as thermodynamics rather than detailed gauge theory states.

Findings

Gravity encodes thermodynamic variables of CFT.

Gravity does not distinguish microstates with same stress tensor.

Explicit relation between 2+1d gravity and 1+1d CFT stress tensor.

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.