The D^{10} R^4 term in type IIB string theory

Abstract

The modular invariant coefficient of the D^{2k} {\cal{R}}^4 term in the effective action of type IIB superstring theory is expected to satisfy Poisson equation on the fundamental domain of SL(2,Z). Under certain assumptions, we obtain the equation satisfied by D^{10} {\cal{R}}^4 using the tree level and one loop results for four graviton scattering in type II string theory. This leads to the conclusion that the perturbative contributions to D^{10} {\cal{R}}^4 vanish above three loops, and also predicts the coefficients at two and three loops.

12 pages, LaTeX

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Cited by in corpus (15)

• Eisenstein series and automorphic representations
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• Constraining Higher Derivative Supergravity with Scattering Amplitudes
• Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes
• The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism
• Duality Groups, Automorphic Forms and Higher Derivative Corrections
• Higher Derivative Supergravities in Diverse Dimensions
• Eisenstein series for infinite-dimensional U-duality groups
• Perturbation Theory From Automorphic Forms
• Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
• Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories
• Higher derivative type II string effective actions, automorphic forms and E11
• Parameters, limits and higher derivative type II string corrections
• Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
• Poisson equations, higher derivative automorphic forms and string parameter limits