# 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:

- 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}

}

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