Gluon scattering amplitudes with instantons and minimal surfaces with topology change

A bstract We study the instanton effect on the gluon scattering amplitudes at strong coupling and large N for the 𝒩 = 4 supersymmetric Yang-Mills theory. According to Alday and Maldacena, the gluon scattering amplitude corresponds holographically to the area of a worldsheet minimal surface in the T-dual AdS 5 geometry. The Yang-Mills instanton introduces an instanton D-brane in the geometry, with which a particular boundary condition for the minimal surface is imposed. We show that the minimal surface undergoes a topology change depending on the size and the gluon momenta, and that the instanton amplitude exhibits a characteristic dependence on gluon momenta. More specifically, we find that when the fixed instanton size modulus ρ is larger than O(√λ /E) where λ is the ’t Hooft coupling and E is the typical momentum of the scattering gluon, due to the topology change of the worldsheet minimal surface, the instanton amplitude is exponentially enhanced as exp( ρE ).