Gluing via Intersection Theory

by Burkhard Eden (Humboldt U., Berlin)

Monday 21 Oct 2024, 13:00 → 15:00 Europe/Berlin

Seminar room 2

Recent advances on the evaluation of higher-point functions in N=4 super Yang-Mills theory by ``integrability'' techniques rest on the concept of hexagon tessellations: the Riemann surfaces on which Feynman graphs would live are triangulated, the elementary tile being the hexagon originally developed for the three-point problem. To correctly reproduce weak-coupling quantum field theory results the tiles need to be glued together passing virtual particles from one to the other. Methods for the analytic evaluation of such gluing processes largely remain to be developed. We investigate whether intersection theory for generalised hypergeometric functions can help.

Specifically, we study once again two series of residues arising in the two-particle gluing of the one-loop five-point function of stress tensor multiplets. In previous work one of these series could be analytically evaluated, but not the other, although it is related by a variable exchange. In this article we derive systems of Pfaffian differential equations on two integral representations arising in the re-summation of the second series. The equations are canonical and can easily be integrated.