Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2022)133
Keywords
Superstrings and Heterotic Strings; Conformal Field Theory; Differential and Algebraic Geometry; String Duality
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New Poincare-series representations have been derived for infinite families of non-holomorphic modular invariant functions, including modular graph forms in the low-energy expansion of closed-string scattering amplitudes at genus one. These series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. The Poincare sums over depth-one integrals extending beyond modular graph forms are described in terms of iterated integrals over holomorphic cusp forms and their L-values in a companion paper.
We derive new Poincare-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one. The Poincare series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. We evaluate the Poincare sums over these iterated Eisenstein integrals of depth one and deduce new representations for all modular graph forms built from iterated Eisenstein integrals at depth two. In a companion paper, some of the Poincare sums over depth-one integrals going beyond modular graph forms will be described in terms of iterated integrals over holomorphic cusp forms and their L-values.
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