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arXiv · 0801.1813

The Berry Phase of D0-Branes

Chris Pedder·Julian Sonner·David Tong
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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.

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Chris Pedder, Julian Sonner, David Tong. 2008-02-04. The Berry Phase of D0-Branes. https://doi.org/10.1088/1126-6708%2F2008%2F03%2F065

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