Entropy of Berenstein-Maldacena-Nastase Strings

TL;DR

This paper defines and analyzes the entropy of BMN strings in a pp-wave background, establishing an upper bound and exploring its behavior through numerical methods, contributing to understanding string entropy in curved backgrounds.

Contribution

It introduces a probability-based entropy definition for BMN strings and proves a universal logarithmic growth bound in the strong coupling limit.

Findings

Entropy grows at most logarithmically with string coupling

Numerical analysis reveals salient features of string entropy

Provides a probabilistic interpretation for higher genus amplitudes

Abstract

In a previous paper, we proposed a probability interpretation for higher genus amplitudes of BMN (Berenstein-Maldacena-Nastase) strings in a pp-wave background with infinite negative curvature. This provides a natural definition of the entropy of a BMN string as the Shannon entropy of its corresponding probability distribution. We prove a universal upper bound that the entropy grows at most logarithmically in the strong string coupling limit. We also study the entropy by numerical methods and discuss some interesting salient features.