Fuzzy CP2

Regularization of quantum field theories (QFT’s) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a fuzzy manifold''. Such discretization by quantization is remarkably successful in preserving symmetries and topological features, and altogether overcoming the fermion-doubling problem. In this paper, we report on our work on the fuzzification’’ of the four-dimensional CP2 and its QFT’s. CP2 is not spin, but spin${}_c$. Its Dirac operator has many unique features. They are explained and their fuzzy versions are described.