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2008

Large N_c confinement and turbulence

Blaizot, Jean-Paul, Nowak, Maciej A.

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We suggest that the transition that occurs at large $N_c$ in the eigenvalue distribution of a Wilson loop may have a turbulent origin.

We arrived at this conclusion by studying the complex-valued inviscid Burgers-Hopf equation that corresponds to the Makeenko-Migdal loop equation, and we demonstrate the appearance of a shock in the spectral flow of the Wilson loop eigenvalues.
This picture supplements that of the Durhuus-Olesen transition with a particular realization of disorder.
The critical behavior at the formation of the shock allows us to infer exponents that have been measured recently in lattice simulations by Narayanan and Neuberger in $d=2$ and $d=3$.

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R. Narayanan and H. Neuberger, [hep-th] 0711.4551

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The exact correspondence between JW model and YM 2 was observed by M.A. Nowak, P. Olesen and perhaps several others

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J.-P. Blaizot and M.A. Nowak, in preparation

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2008

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