Supergoop Dynamics

摘要

We initiate a systematic study of the dynamics of multi-particle systems withsupersymmetric Van der Waals and electron-monopole type interactions. Thestatic interaction allows a complex continuum of ground state configurations,while the Lorentz interaction tends to counteract this configurational fluidityby magnetic trapping, thus producing an exotic low temperature phase of matteraptly named supergoop. Such systems arise naturally in $\mathcal{N}=2$ gaugetheories as monopole-dyon mixtures, and in string theory as collections ofparticles or black holes obtained by wrapping D-branes on internal spacecycles. After discussing the general system and its relation to quiver quantummechanics, we focus on the case of three particles. We give an exhaustiveenumeration of the classical and quantum ground states of a probe in anarbitrary background with two fixed centers. We uncover a hidden conservedcharge and show that the dynamics of the probe is classically integrable. Incontrast, the dynamics of one heavy and two light particles moving on a lineshows a nontrivial transition to chaos, which we exhibit by studying thePoincar\'e sections. Finally we explore the complex dynamics of a probeparticle in a background with a large number of centers, observing hints ofergodicity breaking. We conclude by discussing possible implications in aholographic context.