Some properties of the Alday-Maldacena minimum

Abstract

The Alday-Maldacena solution, relevant to the n=4 gluon amplitude in N=4 SYM at strong coupling, was recently identified as a minimum of the regularized action in the moduli space of solutions of the AdS_5 sigma-model equations of motion. Analogous solutions of the Nambu-Goto equations for the n=4 case are presented and shown to form (modulo the reparametrization group) an equally large but different moduli space, with the Alday-Maldacena solution at the intersection of the sigma-model and Nambu-Goto moduli spaces. We comment upon the possible form of the regularized action for n=5. A function of moduli parameters z_a is written, whose minimum reproduces the BDDK one-loop five-gluon amplitude. This function may thus be considered as some kind of Legendre transform of the BDDK formula and has its own value independently of the Alday-Maldacena approach.

10 pages

References in corpus (18)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Dimensionally Regulated Pentagon Integrals
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• One-Loop Corrections to Five-Gluon Amplitudes
• Comments on gluon scattering amplitudes via AdS/CFT
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• New Dual Conformally Invariant Off-Shell Integrals
• Infrared Limit of Gluon Amplitudes at Strong Coupling
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Planar quark scattering at strong coupling and universality
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Some Implications of Perturbative Approach to AdS/CFT Correspondence
• On coincidence of Alday-Maldacena-regularized $\sigma$-model and Nambu-Goto areas of minimal surfaces

Cited by in corpus (21)

• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Generating AdS String Solutions
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• S-duality as a beta-deformed Fourier transform
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
• On spacelike and timelike minimal surfaces in $Ad{S}_n$
• A note on string solutions in AdS_3
• Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations
• Constant mean curvature surfaces in AdS_3
• Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle
• A Numerical Study of Gluon Scattering Amplitudes in N=4 Super Yang-Mills Theory at Strong Coupling
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• On coincidence of Alday-Maldacena-regularized $\sigma$-model and Nambu-Goto areas of minimal surfaces
• Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• Deviation from Alday-Maldacena Duality For Wavy Circle
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Alday-Maldacena duality and AdS Plateau problem
• Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R^{1,2}
• Note About String with Euclidean World-Sheet in AdS(5)xS(5)