Matrix dynamics of fuzzy spheres

TL;DR

The paper studies the dynamics of fuzzy two-spheres in a matrix model with RR-flux, showing that both irreducible and reducible $SU(2)$ representations are stationary but that reducible configurations are marginally stable. It reveals exactly marginal deformations (Y-deformations) that broaden the moduli space and, upon fluctuation analysis, generate tachyonic directions, signaling a condensation process that fuses multiple small spheres into a single large one. By exploring one- and two-parameter dynamical ansätze, the authors demonstrate classical pathways for rolling from reducible to irreducible configurations and discuss how a mass term lifts moduli, yielding SUSY and non-SUSY phases with distinct vacua and tunneling behavior. The work connects these matrix-model vacua to SUGRA duals (Polchinski-Strassler and F1-NS5 systems) and to spherical D2-branes via multiple dual descriptions, highlighting the rich energy landscape and condensation dynamics of fuzzy spheres in RR backgrounds.

Abstract

We study the dynamics of fuzzy two-spheres in a matrix model which represents string theory in the presence of RR flux. We analyze the stability of known static solutions of such a theory which contain commuting matrices and SU(2) representations. We find that irreducible as well as reducible representations are stable. Since the latter are of higher energy, this stability poses a puzzle. We resolve this puzzle by noting that reducible representations have marginal directions corresponding to non-spherical deformations. We obtain new static solutions by turning on these marginal deformations. These solutions now have instability or tachyonic directions. We discuss condensation of these tachyons which correspond to classical trajectories interpolating from multiple, small fuzzy spheres to a single, large sphere. We briefly discuss spatially independent configurations of a D3/D5 system described by the same matrix model which now possesses a supergravity dual.