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

2017, April 10
Marcus Sperling and Harold C. Steinacker
ArXiv Preprint arXiv:1704.02863 [hep-th]

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×K, which is expected to entail 2+1 generations.