Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling

Abstract

We construct numerically the minimal surface in AdS spacetime surrounded by the light-like segments, which are dual to the 4, 6 and 8-point gluon scattering amplitudes in N=4 super Yang-Mills theory. We evaluate the area of the minimal surface in the radial cut-off regularization and compare these areas with the formula conjectured by Bern, Dixon and Smirnov (BDS), which is modified by the remainder function of cross-ratios of external momenta for n(\geq 6)-point amplitudes. In our momentum configuration cross-ratios are constant. We calculate the difference of areas with different conformal boost parameters, which is independent of the remainder function, and find that its dependence on the boost parameter is numerically consistent with the BDS formula.

Latex, 21 pages, 9 figures, some points clarified, a reference added

References in corpus (33)

• Gluon scattering amplitudes at strong coupling
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Generating AdS String Solutions
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Infrared Limit of Gluon Amplitudes at Strong Coupling
• Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture
• Planar quark scattering at strong coupling and universality
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Some properties of the Alday-Maldacena minimum
• Quark scattering amplitudes at strong coupling
• Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling
• On n-point Amplitudes in N=4 SYM
• Gluon scattering in $\mathcal{N}=4$ Super Yang-Mills at finite temperature
• Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations
• Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle
• Gluon Scattering in Deformed N=4 SYM
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• A Numerical Study of Gluon Scattering Amplitudes in N=4 Super Yang-Mills Theory at Strong Coupling
• On coincidence of Alday-Maldacena-regularized $\sigma$-model and Nambu-Goto areas of minimal surfaces
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• Deviation from Alday-Maldacena Duality For Wavy Circle

Cited by in corpus (8)

• Moduli Dynamics of AdS_3 Strings
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• On spacelike and timelike minimal surfaces in $Ad{S}_n$
• Some comments on spacelike minimal surfaces with null polygonal boundaries in $Ad{S}_m$
• Series Solution and Minimal Surfaces in AdS
• Massive quark scattering at strong coupling from AdS/CFT
• Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R^{1,2}
• A short review on TBA equation and scattering amplitude/Wilson loop duality