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arXiv · hep-th/0701057

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

Badis Ydri
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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.

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Badis Ydri. 2007-01-08. Quantum Equivalence of NC and YM Gauge Theories in 2 D and Matrix Theory. https://doi.org/10.1103/physrevd.75.105008

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