String nature of confinement in (non-)abelian gauge theories

Antonov, Dmitri

doi:10.1080/01422410008229119

Cited by 33 publications

(63 citation statements)

References 125 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recent generalization to higher rank gauge fields has been given in [3], [4], [5]. In the non-Abelian case the problem is even more difficult because of the interplay with confinement [6]. Thus, it can be dealt within some appropriate approximation scheme.…”

mentioning

confidence: 99%

p -branes from generalized Yang-Mills theory

Ansoldi

Castro

Spallucci

2001

Class. Quantum Grav.

View full text Add to dashboard Cite

Abstract. We consider the reduced, quenched version of a generalized Yang-Mills action in 4k-dimensional spacetime. This is a new kind of matrix theory which is mapped through the Weyl-Wigner-Moyal correspondence into a field theory over a non-commutative phase space. We show that the "classical" limit of this field theory is encoded into the effective action of an open, (4k−1)-dimensional, bulk brane enclosed by a dynamical, Chern-Simons type, (4k − 2)-dimensional, boundary brane. The bulk action is a pure volume term, while the boundary action carries all the dynamical degrees of freedom.

show abstract

mentioning

confidence: 99%

p -branes from generalized Yang-Mills theory

Ansoldi

Castro

Spallucci

2001

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…In particular, for a flat non-selfintersecting contour C, the double surface integral in this expression becomes S min dσ µν (x) S min dσ µν (x ) = 2Σ 2 , where Σ is the area of the flat surface bounded by C. Thus, one gets the "area-squared" law for the contribution of soft stochastic Yang-Mills fields to a small-sized Wilson-loop average [11][12][13][14][15][16] W(C)…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…In addition to the confining interactions of the stochastic background Yang-Mills fields, which lead to the Wilson-loop average in the form of Equation (15), there also exist non-confining non-perturbative interactions of those fields. To account for the non-confining non-perturbative interactions, one represents the full two-point correlation function of gluonic field strengths as [11][12][13][14][15][16]41]…”

Section: Quark Condensate For Various Heavy Flavorsmentioning

confidence: 99%

“…stems from the cumulant expansion, while the factor of 1/4 is due to the non-Abelian Stokes' theorem. For surfaces at issue, which fit into a circle of size λ, the field-strength tensor F a µν (x) can be treated as constant, so that the correlation function in Equation (2) can be approximated asUsing this parametrization in Equation (2), and noticing that tr T a T b = 1 2 δ ab , one obtainsIn particular, for a flat non-selfintersecting contour C, the double surface integral in this expression becomes S min dσ µν (x) S min dσ µν (x ) = 2Σ 2 , where Σ is the area of the flat surface bounded by C. Thus, one gets the "area-squared" law for the contribution of soft stochastic Yang-Mills fields to a small-sized Wilson-loop average [11][12][13][14][15][16] W(C)Universe 2016, 2, 28 3 of 55Notice that the proportionality of the coefficient at Σ 2 to (gF a µν ) 2 in this formula has for the first time been found in Refs. [17,18].…”

mentioning

confidence: 97%

“…Numerically, the wavelengths of the heavy, i.e., c-, b-, and t-, quarks are smaller than the Yang-Mills vacuum correlation length λ (see the details below), so that the typical Euclidean trajectories of these quarks fit into a circle of diameter λ. To calculate the corresponding small-sized Wilson-loop average, one can use the non-Abelian Stokes' theorem and the cumulant expansion to represent this object as [11][12][13][14][15][16] In this expression, T a is a generator of the fundamental representation of SU(N), and the integrations go over the minimal surface S min bounded by the quark trajectory C. Such a minimal surface is unique for a given contour C, i.e., it is defined by C in an unambiguous way. Furthermore,…”

mentioning

confidence: 99%

See 2 more Smart Citations

World-Line Formalism: Non-Perturbative Applications

Bellettre

2016

Universe

View full text Add to dashboard Cite

This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields.Keywords: the world-line formalism; Wilson loops; analytic calculations of path integrals with the minimal-area surfaces; theoretical foundations of the stochastic vacuum model; confinement and chiral-symmetry breaking in QCD; gluonic bound states; Casimir scaling; the Yang-Mills running coupling; thermodynamics of the gluon plasma; electroweak phase transition Quark Condensate for Various Heavy FlavorsAs is well known, because of confinement in QCD, quarks and gluons do not exist as individual particles, but appear only in the form of bound states (for recent reviews, see [1,2]). The latter include mesons, baryons (as well as other possible quark bound states, such as tetra-and pentaquarks), glueballs, and the so-called hybrids consisting of a quark, an antiquark, and one or several gluons. Each bound state can be represented as an average of a certain operator over the Euclidean QCD vacuum. Since the vacuum state is gauge-invariant, only the gauge-invariant operators yield non-vanishing results once averaged over it. (This statement can be viewed as a corollary of the so-called Elitzur theorem [3,4], which states that a local gauge symmetry cannot be broken spontaneously.) For local composite operators, such asψψ or (F a µν ) 2 , gauge invariance holds automatically, and the mean values of these operators yield the QCD condensates [5,6]. Nevertheless, the quark and the gluon bound states are in general represented by the field operators which are defined at different points of the Euclidean space, so that a phase factor (also called a parallel transporter or a Schwinger string) interpolating between these points is required in order to provide gauge invariance of the full non-local operator. That is, the non-local gauge-invariant operators have, e.g., the formψ i (x)Φ ij xxwhere Φ ij xx and Φ ab xx are the phase factors transforming under the fundamental and the adjoint representations of SU(N), respectively, with i, j = 1, . . . , N and a, b = 1, . . . , N 2 − 1. (Throughout this review, we denote the number of colors by N.) Thus, the phase factors provide long-range correlations of color between individual quark...

show abstract

Confinement of quarks and valence gluons in SU(N) Yang-Mills-Higgs models

Oxman

2013

J. High Energ. Phys.

View full text Add to dashboard Cite

In this work, we analyze a class of Yang-Mills models containing adjoint Higgs fields, with SU (N ) symmetry spontaneously broken down to Z(N ), showing they contain center vortices, Y-junctions formed by them, and junctions where different center vortices are smoothly interpolated by monopole-like configurations. In the context of dual superconductors, these objects represent different states of the gluon field. Center vortices confine quarks to form normal hadron states. The interpolating monopole, which in our model cannot exist as an isolated configuration, is identified with a confined valence gluon. A junction containing a monopole can bind quarks in a color nonsinglet state to form an overall neutral object, identified with a hybrid hadron. These states, formed by quarks bound to a valence gluon, are allowed by QCD, and current experimental collaborations are aimed at identifying them. Finally, considering the general version of the model, based on a compact simple gauge group G, the picture is completed with a heuristic discussion about why it would be natural using as G the dual of the chromoelectric gauge group G e , and external pointlike monopoles to represent the mesonic and baryonic Wilson loops.

show abstract

String nature of confinement in (non-)abelian gauge theories

Cited by 33 publications

References 125 publications

p -branes from generalized Yang-Mills theory

p -branes from generalized Yang-Mills theory

World-Line Formalism: Non-Perturbative Applications

Confinement of quarks and valence gluons in SU(N) Yang-Mills-Higgs models

Contact Info

Product

Resources

About