The Berry Phase of D0-Branes

TL;DR

This paper investigates the Berry phase phenomena in SU(2) supersymmetric quantum mechanics models, revealing how D0-brane dynamics induce non-trivial topological holonomies described by Hopf maps, with implications for anyon statistics and monopole structures.

Contribution

It demonstrates the connection between D0-brane quantum mechanics and topological Berry phases characterized by Hopf maps across different supersymmetry levels.

Findings

D0-brane states acquire Berry holonomies via Hopf maps.

N=2 case leads to anyon statistics with exchange phases +i and -i.

Higher N theories relate to known monopole configurations like Dirac and Yang monopoles.

Abstract

We study SU(2) Yang-Mills quantum mechanics with N=2,4,8 and 16 supercharges. This describes the non-relativistic dynamics of a pair of D0-branes moving in d=3,4,6 and 10 spacetime dimensions respectively. We show that as the D0-branes orbit, states undergo a Berry holonomy described by the four Hopf maps. For the N=2 theory, the associated Hopf map is the Mobius bundle and its effect is to turn the D0-branes into anyons with exchange statistics +i and -i. For the N=4,8 and 16 theories, the Hopf maps give rise to Berry connections that are familiar to physicists: the U(1) Dirac monopole; the SU(2) Yang monopole; and the SO(8) octonionic monopole.