Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2

TL;DR

This paper investigates how quantum instabilities in gauge theories on fuzzy complex projective spaces can induce topology change, focusing on fuzzy CP^2 and phase transitions between different spacetime configurations.

Contribution

It provides a detailed analysis of topology change mechanisms in fuzzy gauge theories, especially on fuzzy CP^2, and explores quantum phase transitions between various spacetime geometries.

Findings

Identification of quantum instabilities leading to topology change.

Detailed phase diagram illustrating transitions between CP^2, S^2, and a point.

Connection between noncommutative interactions and UV-IR mixing effects.

Abstract

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 spacetime 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 CP^2 and discuss at the level of the phase diagram the quantum transitions between the 3 spaces (spacetimes) CP^2, S^2 and the 0-dimensional space consisting of a single point {0}.