Transforming the bootstrap: using transformers to compute scattering amplitudes in planar super Yang–Mills theory

Abstract

We pursue the use of deep learning methods to improve state-of-the-art computations in theoretical high-energy physics. Planar $\mathcal{N} = 4$ Super Yang–Mills theory is a close cousin to the theory that describes Higgs boson production at the Large Hadron Collider; its scattering amplitudes are large mathematical expressions containing integer coefficients. In this paper, we apply transformers to predict these coefficients. The problem can be formulated in a language-like representation amenable to standard cross-entropy training objectives. We design two related experiments and show that the model achieves high accuracy ( ${\gt}{98\%})$ on both tasks. Our work shows that transformers can be applied successfully to problems in theoretical physics that require exact solutions.

Keywords

• transformers
• physics
• scattering amplitudes
• AI
• 𝒩 = 4 planar super Yang–Mills theory
• high-energy physics