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High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT
Abstract:
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.
