A note on non-perturbative R^4 couplings

Abstract

Exact non-perturbative results have been conjectured for R^4 couplings in type II maximally supersymmetric string theory. Strong evidence has already been obtained, but contributions of cusp forms, invisible in perturbation theory, have remained an open possibility. In this note, we use the D=8 N=2 superfield formalism of Berkovits to prove that supersymmetry requires the exact R^4 threshold to be an eigenmode of the Laplacian on the scalar manifold with a definite eigenvalue. Supersymmetry and U-duality invariance then identify the exact result with the order-3/2 Eisenstein series, and rule out cusp form contributions.

6 pages, uses amsmath and amssymb; typo in eq.(2) corrected; final version to be published in Phys. Lett. B

References in corpus (8)

• Effects of D-instantons
• On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
• D-instantons, Strings and M-theory
• One-loop four-graviton amplitude in eleven-dimensional supergravity
• Calculable e^{-1/λ} Effects
• Construction of $R^4$ Terms in N=2 D=8 Superspace
• U-duality and D-brane Combinatorics
• An ansatz for a non-perturbative four-graviton amplitude in type IIB superstring theory

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