On the Significance of the Vector Potential Squared

Gubarev, F. V.; Stodolsky, L.; Захаров, В. И.

doi:10.1103/physrevlett.86.2220

Cited by 272 publications

(423 citation statements)

References 6 publications

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“…This suggests that a non-local dimension two condensate should be formed. In QCD, it has been investigated [27] that the non-zero value for the minimum of the vector potential condensate A 2 , which is defined to be d 3 x A 2 (x) is possible. This dimension two condensate can be shown to be gauge invariant but non-local.…”

Section: Discussionmentioning

confidence: 99%

“…In QCD, the relevant and marginal operators that can form condensates without breaking Lorentz and gauge symmetries at low energies are F a µν F aµν (dimension 4) andqq (dimension 3). The dimension 2 operator condensate A a µ A aµ min [27] will be discussed later. These condensates can be used to parameterize the non-perturbative observables and their effects should not be neglected.…”

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confidence: 99%

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AdS/QCD phenomenological models from a back-reacted geometry

Shock

et al. 2007

J. High Energy Phys.

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We construct a fully back-reacted holographic dual of a four-dimensional field theory which exhibits chiral symmetry breaking. Two possible models are considered by studying the effects of a five-dimensional field, dual to the qq operator. One model has smooth geometry at all radii and the other dynamically generates a cutoff at finite radius. Both of these models satisfy Einstein's field equations. The second model has only three free parameters, as in QCD, and we show that this gives phenomenologically consistent results. We also discuss the possibility that in order to obtain linear confinement from a backreacted model it may be necessary to consider the condensate of a dimension two operator.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

AdS/QCD phenomenological models from a back-reacted geometry

Shock

et al. 2007

J. High Energy Phys.

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“…The asymptotic large distance vacuum value of t is determined by minimizing the Landau-Ginzburg free energy, for example the last term of (9) in soliture would identify the asymptotic value of t to be the circle t 3 = 0 corresponding to equal asymptotic densities ρ 1 = ρ 2 . But in general t 3 = ±1, as we only expect that both asymptotic densities ρ 1 and ρ 2 are non-vanishing [5].…”

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confidence: 99%

“…In a superconductor they describe the densities of the Cooper pairs, and under appropriate conditions the London limit is a reasonable approximation. But in the present case these fields relate to extrema of (2) under gauge transformations, and the SU(2) gauge invariance of the London limit must be justified separately, for example by numerical investigations [5]. Consequently here the London limit is solely an analytically tractable simplification of (9), (11).…”

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confidence: 99%

“…Thus, even though the field ρ is in general a gauge dependent quantity, its extremum values with respect to gauge transformations are manifestly gauge independent when the theory is subject to the Landau version of maximal abelian gauge. Recent numerical investigations indicate that in strong coupling regime the extrema of ρ are nonvanishing [5] The antisymmetric tensor…”

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Dual Superconductors And Su(2) Yang-Mills

Niemi

2004

J. High Energy Phys.

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We propose that the SU(2) Yang-Mills theory can be interpreted as a two-band dual superconductor with an interband Josephson coupling. We discuss various consequences of this interpretation including electric flux quantization, confinement of vortices with fractional flux, and the possibility that a closed vortex loop exhibits exotic exchange statistics. PACS numbers:Color confinement remains one of the great mysteries of modern high energy physics [1]. Several approaches have been proposed to explain why and how a SU(N) Yang-Mills theory supports confining colored strings, including a variety of dual superconductor and central vortex models [2]. But until now the relevant dynamical string degrees of freedom have not been identified.Recently it has been proposed [3] that the string variables in a Yang-Mills theory could relate to an appropriate decomposion of the gauge field. In the simplest case of SU(2) considered here, we start by separating A a µ (a = 1, 2, 3) into its U(1) Cartan component A 3 µ ≡ A µ while the off-diagonal A i µ (i = 1, 2) we combine into the complex variableWe introduce the U(1) covariant derivativesHere we have explicitely displayed a gauge fixing and Faddeev-Popov ghost (P, η) [4] only for the off-diagonal A 1,2 µ components. The remaining Cartan U(1) gauge invariance can be fixed similarly. But we shall find that this U(1) invariance can also be eliminated directly, by casting the Lagrangian in a form that involves only manifestly U(1) invariant variables. In the following we shall mostly exclude the ghosts from explicit equations. Their inclusion has very little if any conceptual impact. For the present purposes it is important to note that the sole effect of the fourth term in the r.h.s. of (1) is a redefinition of the gauge parameter ξ → ξ − 1 in the gauge fixing (fifth) term. Thus these terms can be combined. In particular, in the ξ → ∞ limit the fourth term becomes entirely immaterial. This limit yields the Landau version of the maximal abelian gaugewhich we shall assume has been imposed. We note that this gauge condition appears as the variational equation when one locates the extrema of the functionalwith respect to the full SU(2) gauge transformations. Thus, even though the field ρ is in general a gauge dependent quantity, its extremum values with respect to gauge transformations are manifestly gauge independent when the theory is subject to the Landau version of maximal abelian gauge. Recent numerical investigations indicate that in strong coupling regime the extrema of ρ are nonvanishing [5] The antisymmetric tensor

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Dimension-2 condensates, ζ-regularization and large-Nc Regge models

Arriola

Broniowski

The IVth International Conference on Quarks and Nuclear Physics

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On the Significance of the Vector Potential Squared

Cited by 272 publications

References 6 publications

AdS/QCD phenomenological models from a back-reacted geometry

AdS/QCD phenomenological models from a back-reacted geometry

Dual Superconductors And Su(2) Yang-Mills

Dimension-2 condensates, ζ-regularization and large-Nc Regge models

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