Brane compactifications and 4-dimensional geometry in the IKKT model

Abstract

We study in detail certain brane solutions with compact extra dimensions M^4 x K in the IKKT matrix model, with K being a two-dimensional rotating torus embedded in R^6. We focus on the compactification moduli and the fluctuations of K \subset R^6 and their physical significance. Mediated by the Poisson tensor, they contribute to the effective 4-dimensional metric on the brane, and thereby become gravitational degrees of freedom. We show that the zero modes corresponding to the global symmetries of the model lead to Ricci-flat 4-dimensional metric perturbations, wherever the energy-momentum tensor vanishes. Their coupling to the energy momentum tensor depends on the extrinsic curvature of the brane.

35 pages. V2: improved presentation, published version

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• On the energy-momentum tensor in Moyal space
• Dirac equation on coordinate dependent noncommutative space-time
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• Spinning the Fuzzy Sphere
• A general procedure to find ground state solutions for finite $N$ M(atrix) theory. Reduced models and SUSY quantum cosmology