Scalar Field Theory on Fuzzy S^4

Abstract

Scalar fields are studied on fuzzy $S^4$ and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4 in the fuzzy context.

16 pages, LaTeX

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• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• The fuzzy 4-hyperboloid $H_n^4$ and higher-spin in Yang-Mills matrix models
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Emergent gravity on covariant quantum spaces in the IKKT model
• Geometry of the Grosse-Wulkenhaar Model
• Fuzzy Complex Quadrics and Spheres
• Cosmological space-times with resolved Big Bang in Yang-Mills matrix models
• String states, loops and effective actions in noncommutative field theory and matrix models
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Absence of a fuzzy $S^4$ phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
• Construction of fuzzy S^4
• Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
• Quantum effective potential for U(1) fields on S^2_L X S^2_L
• The beat of a fuzzy drum: fuzzy Bessel functions for the disc
• Uniform order phase and phase diagram of scalar field theory on fuzzy $\mathbb{C}{P}^n$
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
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• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Higher spin gauge theory on fuzzy $S_N^4$
• One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
• Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $C{P}^3$ as a $S_F^2$ bundle over $S_F^4$
• A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$
• Heat kernel coefficients for compact fuzzy spaces
• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• Scalar modes and the linearized Schwarzschild solution on a quantized FLRW space-time in Yang-Mills matrix models
• Intertwining noncommutativity with gravity and particle physics
• Towards Noncommutative Fuzzy QED
• Emergent fuzzy geometry and fuzzy physics in $4$ dimensions
• Matrix Configurations for Spherical 4-branes and Non-commutative Structures on S^4
• A projective Dirac operator on CP^2 within fuzzy geometry
• Fuzzy Torus via q-Parafermion
• On localized and coherent states on some new fuzzy spheres
• Dirac operator on the quantum fuzzy four-sphere $S_{qF}^4$