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
Tianji Cai, G. Merz, François Charton, N. S. Nolte, Matthias Wilhelm, K. Cranmer, Lance J. Dixon
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>></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.