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

Abstract

Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are $\mathrm{SL}(2,\mathbb{Z})$-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. $\mathrm{SL}(2,\mathbb{Z})$-invariance will in turn strongly constrain the behaviour of the non-perturbative sector when expanded at the origin of the moduli space.

arXiv comment40 pages, 3 figures

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Cited by in corpus (4)

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• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
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• Modular Features of Superstring Scattering Amplitudes: Generalised Eisenstein Series and Theta Lifts