### Abstract

The eigenvalues of Wilson loop matrices in SU(N) gauge theories in dimensions 2, 3, 4 at infinite N are supported on a small arc on the unit circle centered at z = 1 for small loops, but expand to the entire unit circle for large loops. These two regimes are separated by a large N phase transition whose universal properties are the same in d = 2; 3 and 4. Hopefully, this large N universality could be exploited to bridge traditional perturbation theory calculations, valid for small loops, with effective string calculations for large loops. A concrete case of such a calculation would obtain analytically an estimate of the large N string tension in terms of the perturbative scale Λ_{SU(N)}.

Original language | English (US) |
---|---|

Pages (from-to) | 3201-3229 |

Number of pages | 29 |

Journal | Acta Physica Polonica B |

Volume | 40 |

Issue number | 12 |

State | Published - Dec 1 2009 |

Event | "49th Cracow School of Theoretical Physics, 'Non-perturbativeGravity and Quantum Chromodynamics'" - Zakopane, Poland Duration: May 31 2009 → Jun 10 2009 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Acta Physica Polonica B*,

*40*(12), 3201-3229.

}

*Acta Physica Polonica B*, vol. 40, no. 12, pp. 3201-3229.

**Large N phase transitions under scaling and their uses.** / Neuberger, Herbert.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Large N phase transitions under scaling and their uses

AU - Neuberger, Herbert

PY - 2009/12/1

Y1 - 2009/12/1

N2 - The eigenvalues of Wilson loop matrices in SU(N) gauge theories in dimensions 2, 3, 4 at infinite N are supported on a small arc on the unit circle centered at z = 1 for small loops, but expand to the entire unit circle for large loops. These two regimes are separated by a large N phase transition whose universal properties are the same in d = 2; 3 and 4. Hopefully, this large N universality could be exploited to bridge traditional perturbation theory calculations, valid for small loops, with effective string calculations for large loops. A concrete case of such a calculation would obtain analytically an estimate of the large N string tension in terms of the perturbative scale ΛSU(N).

AB - The eigenvalues of Wilson loop matrices in SU(N) gauge theories in dimensions 2, 3, 4 at infinite N are supported on a small arc on the unit circle centered at z = 1 for small loops, but expand to the entire unit circle for large loops. These two regimes are separated by a large N phase transition whose universal properties are the same in d = 2; 3 and 4. Hopefully, this large N universality could be exploited to bridge traditional perturbation theory calculations, valid for small loops, with effective string calculations for large loops. A concrete case of such a calculation would obtain analytically an estimate of the large N string tension in terms of the perturbative scale ΛSU(N).

UR - http://www.scopus.com/inward/record.url?scp=77950427886&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950427886&partnerID=8YFLogxK

M3 - Conference article

VL - 40

SP - 3201

EP - 3229

JO - Acta Physica Polonica B

JF - Acta Physica Polonica B

SN - 0587-4254

IS - 12

ER -