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.

13 pages, one graph

References in corpus (1)

• The One-Plaquette Model Limit of NC Gauge Theory in 2D

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• Emergent fuzzy geometry and fuzzy physics in $4$ dimensions
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