Weight bound conjecture for momentum-space Feynman amplitudes

About 11 years old · traced to

Let GG be a Feynman graph with hh loops, let d∈2Nd\in 2\mathbb{N} be the space-time dimension, and let ωG\omega_G be the integrand of its Feynman amplitude. Let ωdRgenWdhmot⁡G\omega^{\mathrm{gen}}_{dR}W_{dh}\operatorname{mot}_G denote the indicated de Rham realization of the weight-dhdh part of the graph motive.

Weight bound conjecture. The amplitude integrand satisfies

ωG∈ωdRgenWdhmot⁡G.\omega_G\in\omega^{\mathrm{gen}}_{dR}W_{dh}\operatorname{mot}_G.

This gives a bound on the weights of amplitudes, rather than of general Feynman periods, which may have higher weights. Together with the stability conjecture, the source says it would imply that the amplitude is a regularised period of motic descendants of degree at most dhdh.

References

Primary source

Francis Brown, “Feynman Amplitudes and Cosmic Galois group”, arXiv:1512.06409 (2017).

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