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

Abstract

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.

Authors:
 [1]
  1. Institut fur Physik, Humboldt-Universitat zu Berlin, Newtonst. 15, D-12489, Berlin (Germany)
Publication Date:
OSTI Identifier:
20933299
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.105008; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Ydri, Badis. Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.105008.
Ydri, Badis. Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory. United States. doi:10.1103/PHYSREVD.75.105008.
Ydri, Badis. Tue . "Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory". United States. doi:10.1103/PHYSREVD.75.105008.
@article{osti_20933299,
title = {Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory},
author = {Ydri, Badis},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.75.105008},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}