The Entropic Principle and Asymptotic Freedom

TL;DR

This paper links the maximization of an entropy functional on Calabi-Yau moduli space to asymptotic freedom in effective theories, revealing a connection with BPS state stability and special geometric structures.

Contribution

It introduces an entropy functional on Calabi-Yau moduli space and demonstrates its maximization correlates with asymptotic freedom and special geometric points.

Findings

Maximization of entropy correlates with asymptotic freedom.

Maximal entropy points align with walls of marginal stability.

Connections to quantum deformed complex multiplication.

Abstract

Motivated by the recent developments about the Hartle-Hawking wave function associated to black holes, we formulate an entropy functional on the moduli space of Calabi-Yau compactifications. We find that the maximization of the entropy is correlated with the appearance of asymptotic freedom in the effective field theory. The points where the entropy is maximized correspond to points on the moduli which are maximal intersection points of walls of marginal stability for BPS states. We also find an intriguing link between extremizing the entropy functional and the points on the moduli space of Calabi-Yau three-folds which admit a `quantum deformed' complex multiplication.