Fuzzy $CP^2$ Space-Times

Understand

Four-dimensional manifolds with changing signature are obtained by taking the large $N$ limit of fuzzy $CP^2$ solutions to a Lorentzian matrix model.

• The regions of Lorentzian signature give toy models of closed universes which exhibit cosmological singularities.
• These singularities are resolved at finite $N$, as the underlying $CP^2$ solutions are expressed in terms of finite matrix elements.