Perturbative type II amplitudes for BPS interactions

Abstract

We consider the perturbative contributions to the R^4, D^4 R^4 and D^6 R^4 interactions in toroidally compactified type II string theory. These BPS interactions do not receive perturbative contributions beyond genus three. We derive Poisson equations satisfied by these moduli dependent string amplitudes. These T--duality invariant equations have eigenvalues that are completely determined by the structure of the integrands of the multi--loop amplitudes. The source terms are given by boundary terms of the moduli space of Riemann surfaces corresponding to both separating and non--separating nodes. These are determined directly from the string amplitudes, as well as from the logarithmic divergences of maximal supergravity. We explicitly solve these Poisson equations in nine and eight dimensions.

33 pages, LaTeX, 2 figures

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Cited by in corpus (9)

• Poisson equation for the three loop ladder diagram in string theory at genus one
• Eigenvalue equation for the modular graph $C_{a,b,c,d}$
• Cancellation of divergences up to three loops in exceptional field theory
• Eigenvalue equation for genus two modular graphs
• Low momentum expansion of one loop amplitudes in heterotic string theory
• Relations between elliptic modular graphs
• String theory integrands and supergravity divergences
• Supergravity limit of genus two modular graph functions in the worldline formalism
• Transcendentality violation in type IIB string amplitudes