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.

40 pages, 3 figures

References in corpus (12)

• Writing CFT correlation functions as AdS scattering amplitudes
• String scattering in flat space and a scaling limit of Yang-Mills correlators
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Modular properties of two-loop maximal supergravity and connections with string theory
• $D^6{R}^4$ amplitudes in various dimensions
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Tetrahedral modular graph functions
• Resurgence of the dressing phase for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Low momentum expansion of one loop amplitudes in heterotic string theory
• Zero mode of the Fourier series of some modular graphs from Poincare series