Eigenvalue equation for the modular graph C_a,b,c,d (Quantum Spacetime Seminar Series)

The modular graph Ca,b,c,d on the torus is a three loop planar graph in which two of the vertices have coordination number four, while the others have coordination number two. We obtain an eigenvalue equation satisfied by Ca,b,c,d for generic values of a,b,c and d. This family of graphs arises in the calculation of one loop amplitudes in superstring theory.