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arXiv · 1803.10250

$D^6R^4$ curvature corrections, modular graph functions and Poincaré series

Olof Ahlén·Axel Kleinschmidt
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Abstract

In this note we study the U-duality invariant coefficient functions of higher curvature corrections to the four-graviton scattering amplitude in type IIB string theory compactified on a torus. The main focus is on the $D^6R^4$ term that is known to satisfy an inhomogeneous Laplace equation. We exhibit a novel method for solving this equation in terms of a Poincaré series ansatz and recover known results in $D=10$ dimensions and find new results in $D<10$ dimensions. We also apply the method to modular graph functions as they arise from closed superstring one-loop amplitudes.

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Olof Ahlén, Axel Kleinschmidt. 2018-03-27. $D^6R^4$ curvature corrections, modular graph functions and Poincaré series. https://doi.org/10.1007/jhep05(2018)194

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