The Geometric Phase and Gravitational Precession of D-Branes

TL;DR

This paper explores the geometric phase in D-brane systems, revealing a connection between Berry's phase, non-Abelian gauge fields, and gravitational precession, bridging quantum and classical descriptions.

Contribution

It demonstrates how Berry's phase in D-branes transitions from a Yang monopole at weak coupling to gravitational precession at strong coupling.

Findings

Berry's phase described by SU(2) connection over R^5

Holonomy transitions from Yang monopole to gravitational precession

Spin connection of D4-branes relates to Berry curvature

Abstract

We study Berry's phase in the D0-D4-brane system. When a D0-brane moves in the background of D4-branes, the first excited states undergo a holonomy described by a non-Abelian Berry connection. At weak coupling this is an SU(2) connection over R^5, known as the Yang monopole. At strong coupling, the holonomy is recast as the classical gravitational precession of a spinning particle. The Berry connection is the spin connection of the near-horizon limit of the D4-branes, which is a continuous deformation of the Yang and anti-Yang monopole.