Matrix dynamics of fuzzy spheres

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 the known static solutions of such a theory which contain commuting matrices and SU(2) representations. We find that the irreducible as well as the reducible representations are stable. Since the latter are of higher energy, this stability poses a puzzle. We resolve this puzzle by noting that the reducible represenations have marginal deformations 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 corresponds 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.