Large N phase transitions under scaling and their uses

Research output: Contribution to journalConference article

2 Citations (Scopus)

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 ΛSU(N).

Original languageEnglish (US)
Pages (from-to)3201-3229
Number of pages29
JournalActa Physica Polonica B
Volume40
Issue number12
StatePublished - Dec 1 2009
Event"49th Cracow School of Theoretical Physics, 'Non-perturbativeGravity and Quantum Chromodynamics'" - Zakopane, Poland
Duration: May 31 2009Jun 10 2009

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scaling
strings
gauge theory
eigenvalues
arcs
perturbation theory
estimates
matrices

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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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 ΛSU(N).",
author = "Herbert Neuberger",
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Large N phase transitions under scaling and their uses. / Neuberger, Herbert.

In: Acta Physica Polonica B, Vol. 40, No. 12, 01.12.2009, p. 3201-3229.

Research output: Contribution to journalConference article

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AU - Neuberger, Herbert

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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).

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