Quantum100 ⊗ AI Workshop

In Yang-Mills theory, which describes the interactions of elementary particles, gluon scattering amplitudes in the presence of an instanton play a crucial role in understanding the phenomenon of confinement and in theoretical calculations for accelerator experiments. It is known that, in the strong coupling and N→∞ limit of N=4 Super Yang-Mills (SYM) theory, the gluon scattering amplitude can be evaluated from the minimal area of a string worldsheet in T-dual AdS space that satisfies specific boundary conditions [Alday, Maldacena, 2007].

We extend this problem by introducing an instanton into this framework, which allows the string to end on a D3-brane that appears in the T-dual AdS space. To solve the problem of optimizing the system while imposing such complex boundary conditions, we utilize the novel AI technique known as Physics-Informed Neural Networks (PINNs). PINNs flexibly and efficiently search for a solution that satisfies all conditions by including the deviation from the required physical constraints—such as the equations of motion, boundary conditions, and symmetries—into the loss function, and then training the neural network to minimize this loss.

Our analysis suggests that when the instanton scale exceeds the gluon wavelength, the amplitude is enhanced compared to the case without an instanton. This result is consistent with the qualitative theoretical estimations.