Geometric and Renormalized Entropy in Conformal Field Theory

TL;DR

This paper explores how to define and compute a renormalized entropy in relativistic quantum field theories, specifically conformal field theories, to address divergence issues and gain insights into black hole information paradox.

Contribution

It introduces a method to define a renormalized entropy in conformal field theories using a moving mirror model, offering a new perspective on quantum information in relativistic settings.

Findings

Renormalized entropy is well-defined as a difference from the ground state.

The moving mirror model illustrates how localized states' entropy differences are finite.

Insights are provided into the black hole information problem.

Abstract

In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the ``information problem'' in black hole physics