Poisson equation for the Mercedes diagram in string theory at genus one

TL;DR

This paper derives a modular invariant Poisson equation for the Mercedes diagram in genus one string theory, linking it to the D^{12} R^4 amplitude and involving complex Feynman diagram calculations.

Contribution

It introduces a novel Poisson equation for the Mercedes diagram, connecting it to one and two loop Feynman diagrams in string theory.

Findings

Derived a modular invariant Poisson equation for the Mercedes diagram

Calculated the diagram's contribution to the D^{12} R^4 amplitude

Connected the diagram's source terms to simpler Feynman diagrams

Abstract

The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three loop Feynman diagram contributes to the D^{12} R^4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one and two loop Feynman diagrams. We calculate its contribution to the D^{12} R^4 amplitude.