Covariant 4-dimensional fuzzy spheres, matrix models and higher spin

Abstract

We study in detail generalized 4-dimensional fuzzy spheres with twisted extra dimensions. These spheres can be viewed as $SO(5)$-equivariant projections of quantized coadjoint orbits of $SO(6)$. We show that they arise as solutions in Yang-Mills matrix models, which naturally leads to higher-spin gauge theories on $S^4$. Several types of embeddings in matrix models are found, including one with self-intersecting fuzzy extra dimensions $S^4\times \mathcal{K}$, which is expected to entail 2+1 generations.

41+7 pages, 4 figures

References in corpus (1)

• Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in $\mathcal{N}=4$ SYM and matrix models

Cited by in corpus (29)

• More on Quantum Chiral Higher Spin Gravity
• One-loop Finiteness of Chiral Higher Spin Gravity
• The fuzzy 4-hyperboloid $H_n^4$ and higher-spin in Yang-Mills matrix models
• Basic introduction to higher-spin theories
• More on Chiral Higher Spin Gravity and Convex Geometry
• Fuzzy de Sitter Space
• Minimal models of field theories: Chiral Higher Spin Gravity
• Higher-Spin Self-Dual Yang-Mills and Gravity from the twistor space
• Higher-spin Yang-Mills, amplitudes and self-duality
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Minimal model of Chiral Higher Spin Gravity
• Chiral Higher Spin Gravity and Convex Geometry
• Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• A Twistorial Description of the IKKT-Matrix Model
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs
• Higher spin gauge theory on fuzzy $S_N^4$
• Constraining higher-spin S-matrices
• Intertwining noncommutativity with gravity and particle physics
• Scalar modes and the linearized Schwarzschild solution on a quantized FLRW space-time in Yang-Mills matrix models
• Infinite distances in multicritical CFTs and higher-spin holography
• Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
• Fuzzy hyperspheres via confining potentials and energy cutoffs
• Contravariant geometry and emergent gravity from noncommutative gauge theories
• The $x_i$-eigenvalue problem on some new fuzzy spheres
• On localized and coherent states on some new fuzzy spheres
• Dirac operator on the quantum fuzzy four-sphere $S_{qF}^4$
• Covariant Star Product on Semi-Conformally Flat Noncommutative Calabi-Yau Manifolds and Noncommutative Topological Index Theorem