Fuzzy Spheres in pp Wave Matrix String Theory

Abstract

The behaviour of matrix string theory in the background of a type IIA pp wave at small string coupling, g_s << 1, is determined by the combination M g_s where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond background. For M g_s << 1, the matrix string theory is conventional; only the degrees of freedom in the Cartan subalgebra contribute, and the theory reduces to copies of the perturbative string. For M g_s >> 1, the theory admits degenerate vacua representing fundamental strings blown up into fuzzy spheres with nonzero lightcone momenta. We determine the spectrum of small fluctuations around these vacua. Around such a vacuum all N-squared degrees of freedom are excited with comparable energies. The spectrum of masses has a spacing which is independent of the radius of the fuzzy sphere, in agreement with expected behaviour of continuum giant gravitons. Furthermore, for fuzzy spheres characterized by reducible representations of SU(2) and vanishing Wilson lines, the boundary conditions on the field are characterized by a set of continuous angles which shows that generically the blown up strings do not ``close''.

45 pages REVTeX 4 and AMSLaTeX. 1 figure. v2: references added. Figure redrawn using LaTeX

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• Quantum gauge theories on noncommutative 3-d space
• Five-Brane Thermodynamics from the Matrix Model
• Free Energy and Phase Transition of the Matrix Model on a Plane-Wave
• Gauge theories on quantum spaces
• Fuzzy 5-spheres and pp-wave Matrix Actions
• Supersymmteric Null-like Holographic Cosmologies
• Dynamical aspects of the plane-wave matrix model at finite temperature
• Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• The Supergravity Dual of the BMN Matrix Model
• Matrix Model in a Class of Time Dependent Supersymmetric Backgrounds
• One-Loop Flatness of Membrane Fuzzy Sphere Interaction in Plane-Wave Matrix Model
• Giant Gravitons in AdS_3 x S^3 x T^4 as Fuzzy Cylinders
• Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions
• Type II pp-wave Matrix Models from Point-like Gravitons
• Topologically Twisted $N=(2,2)$ Supersymmetric Yang-Mills Theory on Arbitrary Discretized Riemann Surface
• Gauge/Gravity Duality for Interactions of Spherical Membranes in 11-dimensional pp-wave
• Matrix Model Thermodynamics
• Dynamics of Antimembranes in the Maximally Supersymmetric Eleven-Dimensional pp Wave
• Giant Gravitons in type IIA PP-wave Background
• Smearing Effect in Plane-Wave Matrix Model
• A one-loop test for construction of 4D N=4 SYM from 2D SYM via fuzzy sphere geometry
• Probing Smearing Effect by Point-Like Graviton in Plane-Wave Matrix Model
• Pp-wave Matrix Models from Point-like Gravitons