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Covariant 4-dimensional fuzzy spheres, matrix models and higher spin (1704.02863v1)

Published 10 Apr 2017 in hep-th, math-ph, and math.MP

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 $S4$. Several types of embeddings in matrix models are found, including one with self-intersecting fuzzy extra dimensions $S4 \times \mathcal{K}$, which is expected to entail 2+1 generations.

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