Transforming the bootstrap: using transformers to compute scattering amplitudes in planar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> super Yang–Mills theory

Abstract

Abstract We pursue the use of deep learning methods to improve state-of-the-art computations in theoretical high-energy physics. Planar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">N</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>&gt;</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>98</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> on both tasks. Our work shows that transformers can be applied successfully to problems in theoretical physics that require exact solutions.