Modular graph forms from equivariant iterated Eisenstein integrals

Daniele Dorigoni

doi:10.1007/JHEP12(2022)162

Modular graph forms from equivariant iterated Eisenstein integrals

2022-12-28

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DOI：10.1007/JHEP12(2022)162

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The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called equivariant iterated Eisenstein integrals. In this work, we provide the first validations beyond depth one of Brown's conjecture that equivariant iterated Eisenstein integrals contain modular graph forms. Apart from a variety of examples at depth two and three, we spell out the systematics of the dictionary and make certain elements of Brown's construction fully explicit to all orders.

Keyword:

Superstrings and Heterotic Strings

Differential and Algebraic Geometry

Modular graph forms from equivariant iterated Eisenstein integrals

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