Quantum Foam and Topological Strings

TL;DR

This paper links topological string theory on Calabi-Yau manifolds with quantum foam via crystal melting models, revealing how microscopic fluctuations shape the quantum geometry at string scales.

Contribution

It provides a novel interpretation connecting crystal melting configurations to quantum gravitational path integrals in string theory.

Findings

Limit shape of melting crystal corresponds to average quantum foam geometry.

Quantum foam exhibits classical behavior at large scales and quantum fluctuations at string scale.

The model offers a new perspective on the geometry and topology fluctuations in string theory.

Abstract

We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral involving fluctuations of Kahler geometry and topology. We show how the limit shape of the melting crystal emerges as the average geometry and topology of the quantum foam at the string scale. The geometry is classical at large length scales, modified to a smooth limit shape dictated by mirror geometry at string scale and is a quantum foam at area scales g_s \alpha'.