Supergoop Dynamics

Abstract

We initiate a systematic study of the dynamics of multi-particle systems with supersymmetric Van der Waals and electron-monopole type interactions. The static interaction allows a complex continuum of ground state configurations, while the Lorentz interaction tends to counteract this configurational fluidity by magnetic trapping, thus producing an exotic low temperature phase of matter aptly named supergoop. Such systems arise naturally in $\mathcal{N}=2$ gauge theories as monopole-dyon mixtures, and in string theory as collections of particles or black holes obtained by wrapping D-branes on internal space cycles. After discussing the general system and its relation to quiver quantum mechanics, we focus on the case of three particles. We give an exhaustive enumeration of the classical and quantum ground states of a probe in an arbitrary background with two fixed centers. We uncover a hidden conserved charge and show that the dynamics of the probe is classically integrable. In contrast, the dynamics of one heavy and two light particles moving on a line shows a nontrivial transition to chaos, which we exhibit by studying the Poincaré sections. Finally we explore the complex dynamics of a probe particle in a background with a large number of centers, observing hints of ergodicity breaking. We conclude by discussing possible implications in a holographic context.

35 pages,11 figures. v2: updated references to include a previous proof of classical integrability, exchanged a figure for a prettier version

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• Black branes in flux compactifications
• The quantum $p$-spin glass model: A user manual for holographers
• Probing Black Hole Microstate Evolution with Networks and Random Walks
• Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution
• Weak gravity at micron scales from dark bubble cosmology and its cosmological consequences
• Replicas, averaging and factorization in the IIB matrix model
• On the Search for Multicenter AdS Black Holes from M-theory