arXiv subjects

Chris Pedder

Publications and source records attributed to Chris Pedder.

4 recordsLinked to original sources

arXiv2008

The Geometric Phase in Supersymmetric Quantum Mechanics

We explore the geometric phase in N=(2,2) supersymmetric quantum mechanics. The Witten index ensures the existence of degenerate ground states, resulting in a non-Abelian Berry connection. We exhibit a non-renormalization theorem which prohibits the connection from receiving perturbative corrections. However, we show that it does receive corrections from BPS instantons. We compute the one-instanton contribution to the Berry connection for the massive CP^1 sigma-model as the potential is varied. This system has two ground states and the associated Berry connection is the smooth SU(2) 't Hooft-Polyakov monopole.

hep-th↗

arXiv2008

Tunneling D0-branes

In the D0-D4-brane system, D0-branes do not tunnel. Instead, they form bound states with the D4-brane, whose ground states are exact. However, the D0-brane quantum mechanics contains a BPS instanton. To what does this solution correspond? We find that such a tunneling solution provides non-perturbative corrections to the Berry phase connection for the first-excited states as the D4-branes are moved adiabatically. We compute this connection for the first four excited states, and show that it gives an emergent SO(5) connection described previously by Tchrakian.

hep-th↗

arXiv2008

The Geometric Phase and Gravitational Precession of D-Branes

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.

hep-th↗

arXiv2008

The Berry Phase of D0-Branes

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.

hep-th↗