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 D6R4 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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Ahlén, O., Kleinschmidt, A. D6R4 curvature corrections, modular graph functions and Poincaré series. J. High Energ. Phys. 2018, 194 (2018). https://doi.org/10.1007/JHEP05(2018)194
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DOI: https://doi.org/10.1007/JHEP05(2018)194