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

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 $D^6{R}^4$ 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.

arXiv comment27 pages

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Cited by in corpus (8)

• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
• Poincaré series for modular graph forms at depth two. II. Iterated integrals of cusp forms
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• To the cusp and back: Resurgent analysis for modular graph functions
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Adinkra Foundation of Component Decomposition and the Scan for Superconformal Multiplets in 11D, N = 1 Superspace