Evolving fuzzy CP^n and lattice n-simplex

Abstract

Generalizing the previous works on evolving fuzzy two-sphere, I discuss evolving fuzzy CP^n by studying scalar field theory on it. The space-time geometry is obtained in continuum limit, and is shown to saturate locally the cosmic holographic principle. I also discuss evolving lattice n-simplex obtained by `compactifying' fuzzy CP^n. It is argued that an evolving lattice n-simplex does not approach a continuum space-time but decompactifies into an evolving fuzzy CP^n.

Typos corrected, 13 pages, no figures, LaTeX

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• Effective local geometric quantities in fuzzy spaces from heat kernel expansions
• Deformation of Matrix Geometry via Landau Level Evolution