Evolving fuzzy CP^n and lattice n-simplex
Naoki Sasakura (YITP, Kyoto Univ.)
TL;DR
This paper explores the evolution of fuzzy complex projective spaces and lattice n-simplices, revealing how these structures relate to continuum space-times and holographic principles in quantum geometry.
Contribution
It introduces the concept of evolving fuzzy CP^n and lattice n-simplices, extending previous work on fuzzy two-spheres and analyzing their continuum limits and geometric properties.
Findings
Evolving fuzzy CP^n saturates the cosmic holographic principle locally.
Lattice n-simplices decompactify into fuzzy CP^n rather than approaching a continuum space-time.
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.
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