Finite Gauge Theory on Fuzzy CP^2

Details Finite Gauge Theory on Fuzzy CP^2 Finite Gauge Theory on Fuzzy CP^2

2004-07-12

arxiv.org/abs/hep-th/0407089v1

Nucl.Phys. B707 (2005) 145-198

Physics

High Energy Physics

High Energy Physics - Theory

42 pages + 17 pages appendix, 1 figure

Scientific paper

10.1016/j.nuclphysb.2004.11.058

We give a non-perturbative definition of U(n) gauge theory on fuzzy CP^2 as a multi-matrix model. The degrees of freedom are 8 hermitian matrices of finite size, 4 of which are tangential gauge fields and 4 are auxiliary variables. The model depends on a noncommutativity parameter 1/N, and reduces to the usual U(n) Yang-Mills action on the 4-dimensional classical CP^2 in the limit N -> \infty. We explicitly find the monopole solutions, and also certain U(2) instanton solutions for finite N. The quantization of the model is defined in terms of a path integral, which is manifestly finite. An alternative formulation with constraints is also given, and a scaling limit as R^4_\theta is discussed.

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