Supergoop Dynamics

TL;DR

This work analyzes the dynamics of supersymmetric multiparticle systems with monopole-type interactions, dubbed supergoop, focusing on ground-state structure, integrability, and chaos across few- and many-center configurations. By deriving the explicit Lagrangian/Hamiltonian fixed by four supercharges and exploring the Coulomb-branch dynamics, the authors demonstrate classical integrability for a probe in a two-center background and a clear chaotic transition in a collinear three-body setup, then extend to many centers to observe trapping and complex phase-space behavior. They connect ground-state counting to Landau degeneracy and quiver quantum mechanics, and discuss holographic implications in AdS/CFT, including potential chaotic signatures and quantum scarring in the dual field theory. The results illuminate a novel glassy-like phase of strongly interacting BPS systems and provide a framework linking microscopic SUSY dynamics, bound-state moduli spaces, and holographic interpretations of chaotic trajectories.

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.

Figures (11)

• Figure 2.1: Examples of ground states for 100 electric $\Gamma_e = (0,1)$ plus 100 magnetic $\Gamma_m = (1,0)$ particles.
• Figure 4.1: Left: Classical moduli space $\mathcal{M}$ in the $\delta_1 - \delta_2$ plane for $\theta_3 \neq 0$. The nature of $\mathcal{M}$ for the different regions is shown in figure \ref{['regions']}. Right: Classical moduli space for $\mathcal{M}$ with $\theta_3 = 0$. In regions i and ii the centers at $z = a$ and $z = -a$ are enclosed respectively.
• Figure 4.2: Classical moduli space in the $\delta_1 - \delta_2$ plane for $\theta_3 \neq 0$. The order of the figures left to right starting at the top are the regions in figure \ref{['phaseplot']}.
• Figure 4.3: Three node quiver with a closed loop (left) and without a closed loop (right).
• Figure 5.1: The Euler-Jacobi flower. The red balls represent the fixed background centers and the blue line represents the classical trajectory of the probe. In this case, the trajectory precesses around only one of the fixed centers.