Causal Boundary Entropy From Horizon Conformal Field Theory

TL;DR

This paper explores how the quantum near-horizon regions of certain spacetimes can be modeled by a 2D conformal field theory, linking horizon entropy to conformal field theory parameters and Planck-scale physics.

Contribution

It establishes a connection between horizon entropy in cosmological spacetimes and a 2D conformal field theory, providing a microscopic explanation consistent with thermodynamics.

Findings

Horizon entropy is proportional to the horizon area.

The central charge and Hamiltonian expectation value are proportional to the horizon area.

A numerical constant fixed by Planck scale physics aligns entropy with the Bekenstein-Hawking formula.

Abstract

The quantum theory of near horizon regions of spacetimes with classical spatially flat, homogeneous and isotropic Friedman-Robertson-Walker geometry can be approximately described by a two dimensional conformal field theory. The central charge of this theory and expectation value of its Hamiltonian are both proportional to the horizon area in units of Newton's constant. The statistical entropy of horizon states, which can be calculated using two dimensional state counting methods, is proportional to the horizon area and depends on a numerical constant of order unity which is determined by Planck scale physics. This constant can be fixed such that the entropy is equal to a quarter of the horizon area in units of Newton's constant, in agreement with thermodynamic considerations.