Numerical study of large-N phase transition of smeared Wilson loops in 4D pure YM theory

Robert Lohmayer, Herbert Neuberger

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

In Euclidean four-dimensional SU(N) pure gauge theory, eigenvalue distributions of Wilson loop parallel transport matrices around closed spacetime curves show non-analytic behavior (a’large-N phase transition’) at a critical size of the curve. We focus mainly on an observable composed of traces of the Wilson loop operator in all totally antisymmetric representations, which is regularized with the help of smearing. By studying sequences of square Wilson loops on a hypercubic lattice with standard Wilson action, it is shown that this observable has a nontrivial continuum limit as a function of the physical size of the loop. We furthermore present (preliminary) numerical results confirming that, for large N, the N dependence in the critical regime is governed by the universal exponents 1/2 and 3/4 as expected (Burgers universality).

Original languageEnglish (US)
JournalProceedings of Science
Volume139
StatePublished - Jan 1 2011
Event29th International Symposium on Lattice Field Theory, Lattice 2011 - Squaw Valley, Lake Tahoe, United States
Duration: Jul 10 2011Jul 16 2011

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curves
gauge theory
eigenvalues
exponents
continuums
operators
matrices

All Science Journal Classification (ASJC) codes

  • General

Cite this

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title = "Numerical study of large-N phase transition of smeared Wilson loops in 4D pure YM theory",
abstract = "In Euclidean four-dimensional SU(N) pure gauge theory, eigenvalue distributions of Wilson loop parallel transport matrices around closed spacetime curves show non-analytic behavior (a’large-N phase transition’) at a critical size of the curve. We focus mainly on an observable composed of traces of the Wilson loop operator in all totally antisymmetric representations, which is regularized with the help of smearing. By studying sequences of square Wilson loops on a hypercubic lattice with standard Wilson action, it is shown that this observable has a nontrivial continuum limit as a function of the physical size of the loop. We furthermore present (preliminary) numerical results confirming that, for large N, the N dependence in the critical regime is governed by the universal exponents 1/2 and 3/4 as expected (Burgers universality).",
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Numerical study of large-N phase transition of smeared Wilson loops in 4D pure YM theory. / Lohmayer, Robert; Neuberger, Herbert.

In: Proceedings of Science, Vol. 139, 01.01.2011.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Numerical study of large-N phase transition of smeared Wilson loops in 4D pure YM theory

AU - Lohmayer, Robert

AU - Neuberger, Herbert

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Y1 - 2011/1/1

N2 - In Euclidean four-dimensional SU(N) pure gauge theory, eigenvalue distributions of Wilson loop parallel transport matrices around closed spacetime curves show non-analytic behavior (a’large-N phase transition’) at a critical size of the curve. We focus mainly on an observable composed of traces of the Wilson loop operator in all totally antisymmetric representations, which is regularized with the help of smearing. By studying sequences of square Wilson loops on a hypercubic lattice with standard Wilson action, it is shown that this observable has a nontrivial continuum limit as a function of the physical size of the loop. We furthermore present (preliminary) numerical results confirming that, for large N, the N dependence in the critical regime is governed by the universal exponents 1/2 and 3/4 as expected (Burgers universality).

AB - In Euclidean four-dimensional SU(N) pure gauge theory, eigenvalue distributions of Wilson loop parallel transport matrices around closed spacetime curves show non-analytic behavior (a’large-N phase transition’) at a critical size of the curve. We focus mainly on an observable composed of traces of the Wilson loop operator in all totally antisymmetric representations, which is regularized with the help of smearing. By studying sequences of square Wilson loops on a hypercubic lattice with standard Wilson action, it is shown that this observable has a nontrivial continuum limit as a function of the physical size of the loop. We furthermore present (preliminary) numerical results confirming that, for large N, the N dependence in the critical regime is governed by the universal exponents 1/2 and 3/4 as expected (Burgers universality).

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