Fuzzy Geometry via the Spinor Bundle, with Applications to Holographic Space-time and Matrix Theory

Abstract

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 (HST), whose fundamental variables are sections of the spinor bundle over a compact Euclidean manifold. The strong holographic principle (SHP) requires the space of these sections to be finite dimensional. We discuss applications of fuzzy spinor geometry to HST and to Matrix Theory.

revised version matching published version, added references, additional introduction to HST, expanded and improved various sections, 18 pages

References in corpus (7)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Towards a quantum theory of de Sitter space
• Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
• Algebraic Quantum Field Theory
• Holographic space-time and its phenomenological implications
• Holographic Space-time from the Big Bang to the de Sitter era
• SUSY and the Holographic Screens

Cited by in corpus (24)

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• The Holographic Space-Time Model of Cosmology
• Holographic Space-Time: The Takeaway
• Holographic Space-Time Does Not Predict Firewalls
• Interferometric Tests of Planckian Quantum Geometry Models
• The Super BMS Algebra, Scattering and Holography
• Holographic Space-time and Black Holes: Mirages As Alternate Reality
• Soft graviton exchange and the information paradox
• Holographic Theory of Accelerated Observers, the S-matrix, and the Emergence of Effective Field Theory
• Holographic Theories of Inflation and Fluctuations
• Holographic Space-time and Newton's Law
• Supersymmetry Breaking and the Cosmological Constant
• Holographic Space-time, Newton's Law and the Dynamics of Black Holes
• Holographic Fluctuations from Unitary de Sitter Invariant Field Theory
• No Firewalls in Holographic Space-Time or Matrix Theory
• Current Algebra on the Conformal Boundary and the Variables of Quantum Gravity
• Holographic Space-time Models in $1+1$ Dimensions
• Microscopic Models of Linear Dilaton Gravity and Their Semi-classical Approximations
• Spinor geometry
• The Temperature/Entropy Connection for Horizons, Massless Particle Scattering, and the Origin of Locality
• Primordial Black Holes as Dark Matter
• Cosmological SUSY Breaking and the Pyramid Schemes
• Holographic Space-time and Quantum Information
• Quantum Entanglement on Cosmological Scale