On the critical points of the entropic principle

TL;DR

This paper analyzes the entropic principle in Calabi-Yau compactifications, demonstrating that all regular critical points of the entropy functional are maxima, thus clarifying the nature of these critical points.

Contribution

It proves that for compact Calabi-Yaus, all regular critical points of the entropy functional are maxima, providing insight into the entropic principle's critical points.

Findings

All regular critical points are maxima.

Clarification of the critical point nature in the entropic principle.

Supports the interpretation of maxima as preferred compactifications.

Abstract

In a recent paper, hep-th/0509109, Gukov et al. introduced an entropy functional on the moduli space of Calabi-Yau compactifications. The maxima of this functional are then interpreted as "preferred" Calabi-Yau compactifications. In this note we show that for compact Calabi-Yaus, all regular critical points of this entropic principle are maxima.