Quantum Equivalence of NC and YM Gauge Theories in 2 D and Matrix Theory

Abstract

We construct noncommutative U(1) gauge theory on the fuzzy sphere S^2_N as a unitary 2N x 2N matrix model. In the quantum theory the model is equivalent to a nonabelian U(N) Yang-Mills theory on a 2 dimensional lattice with 2 plaquettes. This equivalence holds in the " fuzzy sphere" phase where we observe a 3rd order phase transition between weak-coupling and strong-coupling phases of the gauge theory. In the ``matrix'' phase we have a U(N) gauge theory on a single point.

arXiv comment13 pages, one graph

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Cited by in corpus (6)

• Lectures on Matrix Field Theory I
• Localization for Yang-Mills Theory on the Fuzzy Sphere
• Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2
• A Proposal for a Non-Perturbative Regularization of {\cal N}=2 SUSY 4D Gauge Theory
• Emergent fuzzy geometry and fuzzy physics in $4$ dimensions
• Notes on noncommutative supersymmetric gauge theory on the fuzzy supersphere