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 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.

26 pages, 3 figures, uses JHEP.cls; (v2) references added

References in corpus (9)

• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Scaling Limits of the Fuzzy Sphere at one Loop
• Perturbative dynamics on fuzzy S^2 and RP^2
• D-brane Solutions in Non-Commutative Gauge Theory on Fuzzy Sphere
• Open Strings and Non-commutative Geometry of Branes on Group Manifolds
• Matrix description of D-branes on 3-spheres
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Cited by in corpus (21)

• Flux Compactification
• The Giant Inflaton
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Lectures on Branes in Curved Backgrounds
• Supersymmetric embedding of antibrane polarization
• Deep Quantum Geometry of Matrices
• Field Equations of Massless Fields in the New Interpretation of the Matrix Model
• DBI N-flation
• Instantons, supersymmetric vacua, and emergent geometries
• Nonabelian gauge field and dual description of fuzzy sphere
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• Myers Effect and Tachyon Condensation
• Quantum Stabilization of Compact Space by Extra Fuzzy Space
• Thermodynamics on Fuzzy Spacetime
• Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
• Minimal Areas from Entangled Matrices
• Quantum Entropy for the Fuzzy Sphere and its Monopoles
• Emergent Area Laws from Entangled Matrices
• Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions
• Beyond fuzzy spheres
• Matrix equations and trilinear commutation relations