Matrix dynamics of fuzzy spheres

TL;DR

This paper investigates the stability and dynamics of fuzzy two-spheres in a matrix model related to string theory with RR flux, revealing stable configurations, marginal deformations, and tachyonic instabilities leading to sphere condensation.

Contribution

It provides a detailed stability analysis of static fuzzy sphere solutions, introduces new deformed solutions with instabilities, and discusses their physical interpretation in string theory contexts.

Findings

Both irreducible and reducible representations are stable.

Reducible representations have marginal directions leading to deformations.

Tachyonic instabilities drive the condensation from multiple small spheres to a large sphere.

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.