Modular graph functions and asymptotic expansions of Poincaré series
Abstract
In this note we study $SL(2,\mathbb{Z})$-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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2019
- DOI:
- 10.48550/arXiv.1903.09250
- arXiv:
- arXiv:1903.09250
- Bibcode:
- 2019arXiv190309250D
- Keywords:
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- High Energy Physics - Theory;
- Mathematics - Number Theory
- E-Print:
- 33 pages. v2: Updated to match the published version in Communications in Number Theory and Physics