Simplifying the one loop five graviton amplitude in type IIB string theory

Abstract

We consider the D^8 R^5 and D^{10} R^5 terms in the low momentum expansion of the five graviton amplitude in type IIB string theory at one loop. They involve integrals of various modular graph functions over the fundamental domain of SL(2,Z). Unlike the graphs which arise in the four graviton amplitude or at lower orders in the momentum expansion of the five graviton amplitude where the links are given by scalar Green functions, there are several graphs for the D^8 R^5 and D^{10} R^5 terms where two of the links are each given by a derivative of the Green function. Starting with appropriate auxiliary diagrams, we show that these graphs can be expressed in terms of those which do not involve any derivatives. This results in considerable simplification of the amplitude.

24 pages, LaTeX, 26 figures

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• Proving relations between modular graph functions
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• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
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• 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
• Eigenvalue equation for the modular graph $C_{a,b,c,d}$
• Poincaré series for modular graph forms at depth two. II. Iterated integrals of cusp forms
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• Holomorphic subgraph reduction of higher-point modular graph forms
• Eigenvalue equation for genus two modular graphs
• Poisson equations for elliptic modular graph functions
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• Low momentum expansion of one loop amplitudes in heterotic string theory
• To the cusp and back: Resurgent analysis for modular graph functions
• A simplifying feature of the heterotic one loop four graviton amplitude
• Relations between elliptic modular graphs
• Hierarchy of Modular Graph Identities
• Poisson equation for genus two string invariants: a conjecture
• Transcendentality violation in type IIB string amplitudes
• Integrating simple genus two string invariants over moduli space