Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N?

Kiskis, Joe; Narayanan, Rajamani; Neuberger, Herbert

doi:10.1016/j.physletb.2003.08.070

Cited by 113 publications

(159 citation statements)

References 34 publications

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“…Using these estimates, we compared the scaled lattice data with p(s) for fixed f , b, N and V . One such comparison, at f = 0.15, b = 0.361653, L = 4, N = 44 and V = 7 4 with a gap of 0.1229 (4), is shown in Figure 1 and there is good agreement. In spite of the fact that data is needed over the entire range of s to get a good estimate of the skewness and kurtosis, we find agreement between lattice data and the universal estimates to within 5% for the skewness and to within 20% for the kurtosis for a wide range of gap values.…”

Section: The Determination Of F C (L)mentioning

confidence: 74%

“…Recent lattice work has also indicated that specific non-local observables undergo large N phase transitions as they are dilated [3,4] and this happens while the Euclidean spacetime volume stays infinite in all directions. The critical scales are observable dependent; one can imagine associating with these observables an entire family of dilated images and somewhere along the dilation axis the large N transition takes place.…”

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confidence: 99%

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InfiniteNphase transitions in continuum Wilson loop operators

Narayanan¹,

Neuberger²

2006

J. High Energy Phys.

419

499

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We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Λ-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N -universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.

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Section: The Determination Of F C (L)mentioning

confidence: 74%

mentioning

confidence: 99%

InfiniteNphase transitions in continuum Wilson loop operators

Narayanan¹,

Neuberger²

2006

J. High Energy Phys.

419

499

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“…For substantially smaller values of b the system is in a phase disconnected from continuum Yang-Mills theory. We also need to maintain b ≤ 0.369 to be sure that spontaneous Z 4 (N ) breaking at N = ∞ [15] is avoided on all our volumes, including our smallest, 12 4 . We mainly use the range of couplings 0.359 ≤ b ≤ 0.369.…”

Section: Parameter Choicesmentioning

confidence: 99%

Rectangular Wilson loops at large N

Lohmayer

Neuberger

2012

J. High Energ. Phys.

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This work is about pure Yang-Mills theory in four Euclidean dimensions with gauge group SU(N ). We study rectangular smeared Wilson loops on the lattice at large N and relatively close to the large-N transition point in their eigenvalue density. We show that the string tension can be extracted from these loops but their dependence on shape differs from the asymptotic prediction of effective string theory.

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“…One also finds that the deconfinement transition, which is first order for N ≥ 3, becomes sharper on smaller volumes as N increases suggesting [6] that here too one will have a phase transition on a finite volume at N = ∞. Indeed there appears to be a whole hierarchy of finite volume phase transitions at N = ∞ [7,2] which are, we shall argue below, related to the deconfinement transition.…”

Section: Introductionmentioning

confidence: 96%

Strong to weak coupling transitions ofSU(N)gauge theories in2+1dimensions

Bursa

Teper

2006

Phys. Rev. D

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We investigate strong-to-weak coupling transitions in D = 2 + 1 SU(N → ∞) gauge theories, by simulating the corresponding lattice theories with a Wilson plaquette action. We find that there is a strong-to-weak coupling cross-over in the lattice theory that appears to become a third-order phase transition at N = ∞, in a manner that is essentially identical to the Gross-Witten transition in the D = 1 + 1 SU(∞) lattice gauge theory. There is evidence of an additional second order transition developing at N = ∞ at approximately the same coupling, which is connected with Z N monopoles (instantons), thus making it an analogue of the first order bulk transition that occurs in D = 3 + 1 lattice gauge theories for N ≥ 5. We show that as the lattice spacing is reduced, the N = ∞ gauge theory on a finite 3-torus suffers a sequence of (apparently) first-order Z N symmetry breaking transitions associated with each of the tori (ordered by size). We discuss how these transitions can be understood in terms of a sequence of deconfining transitions on ever-more dimensionally reduced gauge theories. We investigate whether the trace of the Wilson loop has a non-analyticity in the coupling at some critical area, but find no evidence for this. However we do find that, just as one can prove occurs in D = 1 + 1, the eigenvalue density of a Wilson loop forms a gap at N = ∞ at a critical value of its trace. The physical implications of this subtle non-analyticity are unclear. This gap formation is in fact a special case of a remarkable similarity between the eigenvalue spectra of Wilson loops in D = 1 + 1 and D = 2 + 1 (and indeed D = 3 + 1): for the same value of the trace, the eigenvalue spectra are nearly identical. This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops.

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Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N?

Cited by 113 publications

References 34 publications

InfiniteNphase transitions in continuum Wilson loop operators

InfiniteNphase transitions in continuum Wilson loop operators

Rectangular Wilson loops at large N

Strong to weak coupling transitions ofSU(N)gauge theories in2+1dimensions

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