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Identities between Modular Graph Forms
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This paper investigates the relations between modular graph forms, which are generalizations of the modular graph functions that were introduced in earlier papers motivated by the structure of the low energy expansion of genus-one Type II superstring amplitudes. These modular graph forms are multiple sums associated with decorated Feynman graphs on the world-sheet torus. The action of standard differential operators on these modular graph forms admits an algebraic representation on the decorations. First order differential operators are used to map general non-holomorphic modular graph functions to holomorphic modular forms. This map is used to provide proofs of the identities between modular graph functions for weight less than six conjectured in earlier work, by mapping these identities to relations between holomorphic modular forms which are proven by holomorphic methods. The map is further used to exhibit the structure of identities at arbitrary weight.
Forward citations
Cited by 3 Pith papers
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From Modular Graph Forms to Iterated Integrals
A tree-based algorithm converts modular graph forms into equivariant iterated Eisenstein integrals, is implemented for topologies up to four vertices, and is used to extract the alpha'^8 zeta3 zeta5 term of the four-g...
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Towards Motivic Coactions at Genus One from Zeta Generators
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple mo...
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Equivariant primitives of Eisenstein series for congruence subgroups
Equivariant primitives of Eisenstein series for principal congruence subgroups are shown to equal the corresponding non-holomorphic Eisenstein series, including new weight-two cases expressed via single-valued logarithms.
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