Tetrahedral modular graph functions

Abstract

The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams. These integrands are modular invariant and understanding the structure of the action of the modular Laplacian on them is important for determining their contribution to string scattering amplitudes. In this paper we study a particular infinite family of such integrands associated with three-loop scalar vacuum diagrams of tetrahedral topology and find closed forms for the action of the Laplacian. We analyse the possible eigenvalues and degeneracies of the Laplace operator by group- and representation-theoretic means.

40 pages. v2: reference added. Version published in JHEP

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Cited by in corpus (6)

• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Low momentum expansion of one loop amplitudes in heterotic string theory
• To the cusp and back: Resurgent analysis for modular graph functions
• Poisson equation for genus two string invariants: a conjecture
• Integrating simple genus two string invariants over moduli space