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arXiv · 2509.10865

Gluon scattering amplitudes with instantons and minimal surfaces with topology change

Koji Hashimoto·Koichi Kyo·Masaki Murata·Gakuto Ogiwara·Norihiro Tanahashi
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Abstract

We study the instanton effect on the gluon scattering amplitudes at strong coupling and large $N$ for the ${\cal N}=4$ 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 ${\cal O}(\sqrtλ/E)$ 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 $\exp(ρE)$.

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Koji Hashimoto, Koichi Kyo, Masaki Murata, Gakuto Ogiwara, Norihiro Tanahashi. 2025-09-16. Gluon scattering amplitudes with instantons and minimal surfaces with topology change. https://arxiv.org/abs/2509.10865

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