A Note on Twistor Integrals
نویسنده
چکیده
This paper is a brief introduction to twistor integrals from a mathematical point of view. It was inspired by a paper of Hodges [H] which we studied in a seminar at Cal Tech directed by Matilde Marcoli. The idea is to write the amplitude for a graph with n loops and 2n + 2 propagators using the geometry of pfaffians for sums of rank 2 alternating matrices. (Hodges considers the case of 1 loop and 4 edges). Why is this of interest to a mathematician? The Feynman amplitude is a period in the sense of arithmetic algebraic geometry. In parametric form, the amplitude integral associated to a graph Γ with N edges and n loops has the form
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