Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory

Journal Article · Tue May 15 00:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.105008· OSTI ID:20933299

Ydri, Badis ^[1]

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1. Institut fur Physik, Humboldt-Universitat zu Berlin, Newtonst. 15, D-12489, Berlin (Germany)

We construct noncommutative U(1) gauge theory on the fuzzy sphere S{sub N}{sup 2} as a unitary 2Nx2N matrix model. In the quantum theory the model is equivalent to a non-Abelian U(N) Yang-Mills theory on a two-dimensional lattice with two 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.

• OSTI ID: 20933299
• Journal Information: Physical Review. D, Particles Fields, Vol. 75, Issue 10; Other Information: DOI: 10.1103/PhysRevD.75.105008; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
FUZZY LOGIC
GAUGE INVARIANCE
MATRICES
PHASE TRANSFORMATIONS
SPHERES
STRONG-COUPLING MODEL
TWO-DIMENSIONAL CALCULATIONS
U-1 GROUPS
WEAK-COUPLING MODEL
YANG-MILLS THEORY