Comments on gluon 6-point scattering amplitudes in 𝒩 = 4 SYM at strong coupling

Astefanesei, Dumitru; Dobashi, Suguru; Ito, Katsushi; Năstase, Horaţiu

doi:10.1088/1126-6708/2007/12/077

Cited by 27 publications

(42 citation statements)

References 44 publications

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“…Let us now return to the analysis of the cusp divergences of the light-like Wilson loops and take advantage of both the axial gauge and the exponentiation (20). A characteristic feature of the 'webs' following from their maximal non-Abelian nature is that the corresponding Feynman integrals have 'maximally complicated' momentum loop flow.…”

Section: All-loop Structurementioning

confidence: 99%

“…This generates new interaction vertices inside the Feynman diagrams for W n J but does not affect the non-Abelian exponentiation property (20).…”

Section: Structure Of the Anomaly To All Loopsmentioning

confidence: 99%

“…14 The only difference compared with (20) is that the webs w (k) now depend on J(x) through a new interaction vertex. Making use of non-Abelian exponentiation, we obtain…”

Section: Structure Of the Anomaly To All Loopsmentioning

confidence: 99%

“…[14,15,16]), although the practical evaluation of the corresponding solution of the classical string equations is difficult even for n = 5 (for a recent discussion see Refs. [17,18,19,20,21,22,23]). However, Alday and Maldacena [13] proposed a way to do this for very large n, which gives a disagreement with the BDS conjecture at strong coupling.…”

Section: Introductionmentioning

confidence: 99%

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Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

Drummond¹,

Henn²,

Korchemsky³

et al. 2010

Nuclear Physics B

346

660

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Planar gluon amplitudes in N = 4 SYM are remarkably similar to expectation values of Wilson loops made of light-like segments. We argue that the latter can be determined by making use of the conformal symmetry of the gauge theory, broken by cusp anomalies. We derive the corresponding anomalous conformal Ward identities valid to all loops and show that they uniquely fix the form of the finite part of a Wilson loop with n cusps (up to an additive constant) for n = 4 and 5 and reduce the freedom in it to a function of conformal invariants for n ≥ 6. We also present an explicit two-loop calculation for n = 5. The result confirms the form predicted by the Ward identities and matches the finite part of the two-loop five-gluon planar MHV amplitude, up to a constant. This constitutes another non-trivial test of the Wilson loop/gluon amplitude duality.

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Section: All-loop Structurementioning

confidence: 99%

“…This generates new interaction vertices inside the Feynman diagrams for W n J but does not affect the non-Abelian exponentiation property (20).…”

Section: Structure Of the Anomaly To All Loopsmentioning

confidence: 99%

“…14 The only difference compared with (20) is that the webs w (k) now depend on J(x) through a new interaction vertex. Making use of non-Abelian exponentiation, we obtain…”

Section: Structure Of the Anomaly To All Loopsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

Drummond¹,

Henn²,

Korchemsky³

et al. 2010

Nuclear Physics B

346

660

View full text Add to dashboard Cite

show abstract

“…In a previous paper [9], the authors including the two authors in the present paper, constructed solutions for the 6 and 8-point amplitudes by cutting and gluing the 4-point amplitude. The evaluation of the amplitudes shows that they do…”

Section: Introductionmentioning

confidence: 99%

A numerical study of gluon scattering amplitudes in 𝒩 = 4 super Yang-Mills theory at strong coupling

Dobashi¹,

Ito

Iwasaki

2008

J. High Energy Phys.

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We study gluon scattering amplitudes in N = 4 super Yang-Mills theory at strong coupling via the AdS/CFT correspondence. We solve numerically the discretized Euler-Lagrange equations on the square worldsheet for the minimal surface with light-like boundaries in AdS spacetime. We evaluate the area of the surface for the 4, 6 and 8-point amplitudes using worldsheet and radial cut-off regularizations. Their infrared singularities in the cut-off regularization are found to agree with the analytical results near the cusp less than 5% at 520×520 lattice points. Recently Alday and Maldacena[1] proposed the prescription for the calculation of gluon scattering amplitudes in N = 4 super Yang-Mills (SYM) theory at strong coupling via the AdS/CFT correspondence. They showed that the gluon scattering amplitude is related to the area of a minimal surface in AdS spacetime surrounded by the Wilson loop with lightlike boundaries. They found the exact solution of the minimal surface corresponding to the 4-point amplitude and showed that it reproduces the perturbative formula conjectured by Bern, Dixon and Smirnov (BDS) [2]. The correspondence between gluon amplitudes and the Wilson loops has been examined also at weak coupling[3]. It is shown in [4] that the Wilson loops at weak coupling obey the anomalous conformal Ward identity, which determines the n = 4 and 5-point amplitudes completely. For n ≥ 6-point amplitudes, however, the conformal invariance of the amplitudes does not fix their dependence on the kinematical variables. Recently it is found that the 6-point 2-loop corrections to the Wilson loop agrees numerically with the gluon amplitudes but they differ from the BDS formula[5].In order to study gluon scattering amplitudes at strong coupling using the AdS/CFT correspondence, we need to find the solution of the minimal surface in AdS spacetime surrounded by the light-like Wilson loop. See [6,7,8,9,10,11,12,15] for references. The minimal surface is obtained by solving the Euler-Lagrange equations with the Dirichlet boundary conditions. These are non-linear partial differential equations and highly nontrivial to solve analytically for the polygon with n ≥ 5 boundaries. Any exact solution for n ≥ 5 is not yet known so far. In a previous paper [9], the authors including the two authors in the present paper, constructed solutions for the 6 and 8-point amplitudes by cutting and gluing the 4-point amplitude. The evaluation of the amplitudes shows that they do not agree with the BDS formula both for the infrared singularity and finite parts. In particular, the infrared singularities coincide with those of the 4-point amplitudes, which suggests that these simple solutions are not the minimal surfaces and might correspond to the other disconnected amplitudes.In this paper we will propose a practical approach to compute the minimal surface in AdS spacetime. We investigate numerically the solution of the Euler-Lagrange equations

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Some comments on spacelike minimal surfaces with null polygonal boundaries in AdS m

Dorn

2010

J. High Energ. Phys.

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We discuss some geometrical issues related to spacelike minimal surfaces in AdS m with null polygonal boundaries at conformal infinity. In particular for AdS 4 , two holomorphic input functions for the Pohlmeyer reduced system are identified. This system contains two coupled differential equations for two functions α(z,z) and β(z,z), related to curvature and torsion of the surface. Furthermore, we conjecture that, for a polynomial choice of the two holomorphic functions, the relative positions of their zeros encode the conformal invariant data of the boundary null 2n-gon.

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Comments on gluon 6-point scattering amplitudes in 𝒩 = 4 SYM at strong coupling

Cited by 27 publications

References 44 publications

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

A numerical study of gluon scattering amplitudes in 𝒩 = 4 super Yang-Mills theory at strong coupling

Some comments on spacelike minimal surfaces with null polygonal boundaries in AdS m

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