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arXiv · 2208.14087

To the cusp and back: Resurgent analysis for modular graph functions

Daniele Dorigoni·Axel Kleinschmidt·Rudolfs Treilis
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Abstract

Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-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 when the argument of the modular graph function approaches the cusp on this moduli space. ${\rm SL}(2,\mathbb{Z})$-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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Daniele Dorigoni, Axel Kleinschmidt, Rudolfs Treilis. 2022-08-30. To the cusp and back: Resurgent analysis for modular graph functions. https://doi.org/10.1007/jhep11(2022)048

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