Finite Gauge Theory on Fuzzy CP²

2004/07/12 by Harald Grosse, Harold Steinacker · 1 citation
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2004.11.058

published as Nucl.Phys. B707 (2005) 145-198 · 42 pages + 17 pages appendix, 1 figure

arxiv created 2004/07/12 · arxiv updated 2009/12/01

Abstract

We give a non-perturbative definition of U(n) gauge theory on fuzzy CP² 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 CP² in the limit N -> ∞. 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 R⁴_θis discussed.

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