Geometric and Renormalized Entropy in Conformal Field Theory

TL;DR

The paper addresses how entropy is defined and regulated in relativistic quantum field theories with horizons or boundaries, focusing on geometric entropy and its renormalization. By analyzing 1+1D conformal field theories with moving mirror boundaries, it derives an exact logarithmic divergence for geometric entropy and introduces a finite renormalized entropy for excited states, linking it to energy-momentum correlations. The moving-mirror framework is then connected to black hole physics, showing Hawking-like radiation and correlation structures while arguing that renormalized entropy provides a more faithful measure of information content than naive thermodynamic entropy. The work highlights non-additivity and potential negative locally defined entropy, and discusses energy-conservation constraints that challenge simplistic evaporation pictures.

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