Topology change from quantum instability of gauge theory on fuzzy CP2

Many gauge theory models on fuzzy complex projective spaces will contain a strong instability in the quantum field theory leading to topology change. This can be thought of as due to the interaction between space-time via its noncommutativity and the fields (matrices) and it is related to the perturbative UV-IR mixing. We work out in detail the example of fuzzy CP2 and discuss at the level of the phase diagram the quantum transitions between the 3 spaces (space-times) CP2, S2 and the 0-dimensional space consisting of a single point {0}.