Fuzzy geometry via the spinor bundle, with applications to holographic space-time and matrix theory

Journal Article · Sat Oct 15 04:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.84.086008· OSTI ID:21611517

Banks, Tom ^[1]; Kehayias, John ^[2]

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1. NHETC and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019 (United States)
2. SCIPP and Department of Physics, University of California, Santa Cruz, California 95064-1077 (United States)

We present a new framework for defining fuzzy approximations to geometry in terms of a cutoff on the spectrum of the Dirac operator, and a generalization of it that we call the Dirac-flux operator. This framework does not require a symplectic form on the manifold, and is completely rotation invariant on an arbitrary n-sphere. The framework is motivated by the formalism of holographic space-time, whose fundamental variables are sections of the spinor bundle over a compact Euclidean manifold. The strong holographic principle requires the space of these sections to be finite dimensional. We discuss applications of fuzzy spinor geometry to holographic space-time and to matrix theory.

• OSTI ID: 21611517
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 84; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
CALCULATION METHODS
DIRAC OPERATORS
EUCLIDEAN SPACE
HOLOGRAPHY
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MOTION
QUANTUM OPERATORS
RIEMANN SPACE
ROTATION
SPACE
SPACE-TIME
SPECTRA