Modular graph functions and asymptotic expansions of Poincare' series

Dorigoni, Daniele; Kleinschmidt, Axel

Abstract

In this note we study SL(2,Z)-invariant functions such as modular graph functions or coefficient functions of higher derivative corrections in type IIB string theory. The functions solve inhomogeneous Laplace equations and we choose to represent them as Poincaré series. In this way we can combine different methods for asymptotic expansions and obtain the perturbative and non-perturbative contributions to their zero Fourier modes. In the case of the higher derivative corrections, these terms have an interpretation in terms of perturbative string loop effects and pairs of instantons/anti-instantons.

Citation

Dorigoni, D., & Kleinschmidt, A. (2019). Modular graph functions and asymptotic expansions of Poincare' series. Communications in Number Theory and Physics, 13(3), 569-617

• Journal Article Type: Article
• Acceptance Date: Jun 11, 2019
• Online Publication Date: Sep 17, 2019
• Publication Date: Jan 1, 2019
• Deposit Date: Apr 1, 2019
• Publicly Available Date: Oct 3, 2019
• Journal: Communications in Number Theory and Physics
• Print ISSN: 1931-4523
• Electronic ISSN: 1931-4531
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 3
• Pages: 569-617
• Public URL: https://durham-repository.worktribe.com/output/1305125
• Publisher URL: https://www.intlpress.com/site/pub/pages/journals/items/cntp/content/vols/0013/0003/a003/index.php