Abstract
Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are SL(2, ℤ)-invariant functions of the torus complex structure that have to be integrated over the moduli space of inequivalent tori. We use methods from resurgent analysis to construct the non-perturbative corrections arising for two-loop modular graph functions when the argument of the function approaches the cusp on this moduli space. SL(2, ℤ)-invariance will in turn strongly constrain the behaviour of the non-perturbative sector when expanded at the origin of the moduli space.
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Dorigoni, D., Kleinschmidt, A. & Treilis, R. To the cusp and back: resurgent analysis for modular graph functions. J. High Energ. Phys. 2022, 48 (2022). https://doi.org/10.1007/JHEP11(2022)048
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DOI: https://doi.org/10.1007/JHEP11(2022)048