Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling

Abstract

In this note we consider minimal surfaces in three dimensional anti-de Sitter space that end at the AdS boundary on a polygon given by a sequence of null segments. The problem can be reduced to a certain generalized Sinh-Gordon equation and to SU(2) Hitchin equations. The mathematical problem to be solved arises also in the context of the moduli space of certain three dimensional supersymmetric theories. We can use explicit results available in the literature in order to find the explicit answer for the area of a surface that ends on a eight-sided null Wilson loop. Via the gauge/gravity duality this can also be interpreted as a certain eight-gluon scattering amplitude at strong coupling for a special kinematic configuration.

arXiv comment9 pages

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• Scattering into the fifth dimension of N=4 super Yang-Mills
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Moduli Dynamics of AdS_3 Strings
• Simplicity of Polygon Wilson Loops in N=4 SYM
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Space-like minimal surfaces in AdS x S
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• Double-helix Wilson loops: case of two angular momenta
• Series Solution and Minimal Surfaces in AdS
• Massive quark scattering at strong coupling from AdS/CFT
• Giant Holes
• Irregular Singularities in the H3+ WZW Model
• Holographic correlation functions of hexagon Wilson loops with one local operator
• AdS String: Classical Solutions and Moduli Dynamics
• Multi-trace Correlators from Permutations as Moduli Space