Fuzzy CP2

TL;DR

This paper explores the quantization of the four-dimensional CP2 manifold into a fuzzy manifold, preserving symmetries and topological features, and discusses the unique properties of its Dirac operator and its fuzzy version.

Contribution

It introduces the fuzzification of four-dimensional CP2 and its quantum field theories, highlighting the unique features of its Dirac operator and their fuzzy analogs.

Findings

Successful discretization preserving symmetries

Unique features of CP2 Dirac operator explained

Fuzzy versions of Dirac operator described

Abstract

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.