Wilson loops and minimal surfaces

Drukker, Nadav; Gross, David J.; Ooguri, Hirosi

doi:10.1103/physrevd.60.125006

Cited by 497 publications

(952 citation statements)

References 29 publications

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“…If one alternatively uses an unmodified cutoff according to (9), one gets an unwanted factor 1 2 in front of the squared logarithms, as in (6). It would be interesting to find out, whether this effect is related to the different soft regions for the scattering amplitude mentioned in [2].…”

Section: Introductionmentioning

confidence: 99%

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Matching gluon scattering amplitudes and Wilson loops in off-shell regularization

Dorn

Wiesmann

2008

Physics Letters B

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We construct a regularization for light-like polygonal Wilson loops in N = 4 SYM, which matches them to the off-shell MHV gluon scattering amplitudes. Explicit calculations are performed for the 1-loop four gluon case. The off light cone extrapolation has to be based on the local supersymmetric Wilson loop. The observed matching concerns Feynman gauge. Furthermore, the leading infrared divergent term is shown to be gauge parameter independent on 1-loop level.

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Section: Introductionmentioning

confidence: 99%

“…As long as the sides of the polygon are light-like the scalars decouple. Therefore, one can use either the Wilson loop for gauge fields A µ only, or the local supersymmetric Wilson loop coupling to A µ and the scalars φ I [5,6] …”

Section: Introductionmentioning

confidence: 99%

Matching gluon scattering amplitudes and Wilson loops in off-shell regularization

Dorn

Wiesmann

2008

Physics Letters B

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“…The Reggeon-exchange scattering amplitude is obtained by summing up the contributions of these loops, through a path-integration over the trajectories of the exchanged fermions, and performing an appropriate analytic continuation to Minkowski space-time. An estimate of the Reggeon-exchange amplitude is then obtained, by relating the Wilson-loop expectation value, via gauge/gravity duality, to minimal surfaces in a curved confining metric [34,35,36,37,38,39,40], having the loop contour as boundary, and by evaluating the path integral by means of a saddlepoint approximation. The resulting amplitude is of Regge-pole type with a linear Regge trajectory in the massless-quark case [30]; the inclusion of the effects of a nonzero quark mass leaves unchanged the linearity and the slope of the trajectory, while modifying the slope of the amplitude at t = 0 and its shrinkage with energy [31].…”

Section: Introductionmentioning

confidence: 99%

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Giordano

2012

J. High Energ. Phys.

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We derive a nonperturbative expression for the non-vacuum, qq-Reggeon-exchange contribution to the meson-meson elastic scattering amplitude at high energy and low momentum transfer, in the framework of QCD. Describing the mesons in terms of colourless qq dipoles, the problem is reduced to the two-fermion-exchange contribution to the dipole-dipole scattering amplitudes, which is expressed as a path integral, over the trajectories of the exchanged fermions, of the expectation value of a certain Wilson loop. We also show how the resulting expression can be reconstructed from a corresponding quantity in the Euclidean theory, by means of analytic continuation. Finally, we make contact with previous work on Reggeon exchange in the gauge/gravity duality approach.

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“…The classical solutions are found in global Lorentzian AdS 5 6 starting from a time-independent ansatz, the boundary conditions being lines separated by π − φ on the boundary of AdS and θ on S 5 . The relevant solutions (written down in the case of θ = 0 in [19] and for θ = 0 in Appendix C.2 of [24]) can be found for arbitrary values of φ and θ as the solutions of transcendental equations. The result for the generalized potential is then found in 2 In [17], an integral equation was written whose solution gives the contribution of ladder graphs to all orders in perturbation theory.…”

Section: Results At Weak and At Strong Couplingmentioning

confidence: 99%

“…The result for the generalized potential is then found in 2 In [17], an integral equation was written whose solution gives the contribution of ladder graphs to all orders in perturbation theory. 3 The calculation of V (1) at one-loop order was done in [19]. The θ = 0 case is in [17] (see also [20]), where expressions were written in integral form.…”

Section: Results At Weak and At Strong Couplingmentioning

confidence: 99%

Generalized quark‐antiquark potential in AdS/CFT

Форини

Drukker

2012

Fortschritte der Physik

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Key words AdS/CFT correspondence, supersymmetric gauge theory.In this talk we present a family of Wilson loop operators which continuously interpolates between the 1/2 BPS line and the antiparallel lines, and can be thought of as calculating a generalization of the quarkantiquark potential for the gauge theory on S 3 × R. We evaluate the first two orders of these loops perturbatively both in the gauge and string theory. We obtain analytical expressions in a systematic expansion around the 1/2 BPS configuration, and comment on possible all-loop patterns for these Wilson loops.Copyright line will be provided by the publisher OverviewOne of the most fundamental observables in a quantum field theory is the potential between charged particles, which in a gauge theory is captured by a long rectangular Wilson loop, or a pair of antiparallel lines representing the trajectories of infinitely heavy quarks. Such quark-antiquark potential can be also considered in the maximally supersymmetric N = 4 SYM theory, where "quarks" are modeled by infinitely massive W-bosons arising from a Higgs mechanism [1].The expectation value of this observable was calculated very early after the introduction of the AdS/CFT correspondence by the effective action of a string ending along the curve on the four-dimensional AdS boundary, and is in fact a seminal example of the duality itself. In this context of a conformal field theory the potential is fixed to be Coulomb-like and the whole dynamical content is in the corresponding coefficient, for which the weak and strong coupling ('t Hooft coupling λ) previously obtained results readAbove, L is the distance between the lines, K is the complete elliptic integral of the first kind and the weakcoupling expansion is the field-theoretical calculation of [2,3,4]. On the string theory (strong coupling) side, the question of evaluating the first quantum string correction a 1 to the classical result of [1] 1 is a hard mathematical problem. The absence of parameters in the problem (the only one, L, being fixed by conformal invariance) precludes considering special scaling limits in which nice results in σ-model perturbation theory have been obtained for some relevant string solutions (see, for example, [6,7] and reference therein). The coefficient a 1 was presented formally in [8,9], evaluated numerically in [10] to be a 1 = 1.33459 and simplified further in [11] to an analytic one-dimensional integral representation. * Corresponding author vforini@icc.ub.edu * * nadav.drukker@kcl.ac.uk 1 This is actually the AdS 5 ×S 5 counterpart of the so-called "Lüscher term", which in flat space is a coulombic term proportional to the number of transverse dimensions [5].

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Wilson loops and minimal surfaces

Cited by 497 publications

References 29 publications

Matching gluon scattering amplitudes and Wilson loops in off-shell regularization

Matching gluon scattering amplitudes and Wilson loops in off-shell regularization

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Generalized quark‐antiquark potential in AdS/CFT

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