Renormalizability of phase factors in non-abelian gauge theory

Dotsenko, Victor; Vergeles, S. N.

doi:10.1016/0550-3213(80)90103-0

Cited by 330 publications

(464 citation statements)

References 8 publications

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“…The exponent E equals a sum over web diagrams, d, each given by a group factor multiplied by a diagrammatic integral, In momentum space we can write the exponent E as the integral over a single, overall loop momentum that runs through the web and the cusp vertex, assuming that all loop integrals internal to the web have already been carried out. The web is defined to include the necessary counterterms of the gauge theory [8,30,33,34]. Taking into account the boost invariance of the cusp for massless loop velocities, and the invariance of the ordered exponentials under rescalings of the velocities β i , we have for the exponent the form,…”

Section: Exponentiation and Momentum Space Websmentioning

confidence: 99%

Gauge theory webs and surfaces

Erdoǧan

Sterman

2015

Phys. Rev. D

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Section: Exponentiation and Momentum Space Websmentioning

confidence: 99%

Gauge theory webs and surfaces

Erdoǧan

Sterman

2015

Phys. Rev. D

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“…In particular, all colour factors appearing in the exponent correspond to connected graphs [93]. There are two complementary approaches to exponentiation: one is based on evolution equations [2-15, 18, 19, 21-40], which are ultimately a consequence of multiplicative renormalizability [94][95][96][97], and the second is a diagrammatic approach, the direct computation of the exponent in terms of webs [93,[98][99][100][101][102][103][104]. Following ref.…”

Section: Jhep04(2014)044mentioning

confidence: 99%

From webs to polylogarithms

Gardi

2014

J. High Energ. Phys.

186

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We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1/α ij , at the level of the symbol the result also admits a crossing symmetry α ij → −α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and 1 − α 2 ij . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

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“…The first constant term may be included in the self energies of the heavy quarks [41,42]. An unlimited extension of a linear potential to large distances would lead to too strong a van der Waals force between hadrons [43] so that the potential should cease to be linear and fall off at large distances as remarked in the beginning of this subsection.…”

Section: T He CCC and The Linear Potentialmentioning

confidence: 99%

Renormalization constant of the color gauge field as a probe of confinement

Chaichian

Nishijima²

2001

Eur. Phys. J. C

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The mechanism of color confinement as a consequence of an unbroken non-abelian gauge symmetry and asymptotic freedom is elucidated and compared with that of other models based on an analogy with the type II superconductor. It is demonstrated that a sufficient condition for color confinement is given by Z −1 3 = 0 where Z 3 denotes the renormalization constant of the color gauge field. It is shown that this condition is actually satisfied in quantum chromodynamics and that some of the characteristic features of other models follow from it.

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Renormalizability of phase factors in non-abelian gauge theory

Cited by 330 publications

References 8 publications

Gauge theory webs and surfaces

Gauge theory webs and surfaces

From webs to polylogarithms

Renormalization constant of the color gauge field as a probe of confinement

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