Hierarchy of Modular Graph Identities

Understand

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus.

• In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed.
• In the present paper, these results are generalized in two complementary directions.
• First, all identities at weight six and all dihedral identities at weight seven are obtained and proven.