Type IIB $R^4{H}^{4g-4}$ Conjectures

Abstract

We propose $SL(2,Z)$ (and $SL(3,Z)$) invariant conjectures for all $R^4{H}^{4g-4}$ couplings of Type IIB strings on $R^{10}$ (and $R^8\times T^2$), generalizing conjectures of Green and Gutperle (and Kiritsis and Pioline) for the $R^4$ coupling. A strong check for our conjectures is that on $T^2$ at weak coupling, they reproduce the multiloop scattering amplitudes which had been previously computed using N=2 strings in the N=4 topological formalism. Applications to $(p,q)$ string production in a background $H$ field, generalizing Schwinger's computation for pair production in constant $F$ field, are suggested.

Added three references

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• On a supersymmetric completion of the $R^4$ term in type IIB supergravity
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• N=4 Topological Amplitudes and String Effective Action
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• Perturbation Theory From Automorphic Forms
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• Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
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• A Curious Truncation of N=4 Yang-Mills
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