Higher Derivative Couplings and Heterotic-Type I Duality in Eight Dimensions

Abstract

We calculate F^4 and R^4T^(4g-4) couplings in d=8 heterotic and type I string vacua (with gauge and graviphoton field strengths F,T, and Riemann curvature R). The holomorphic piece F_g of the heterotic one-loop coupling R^4T^(4g-4) is given by a polylogarithm of index 5-4g and encodes the counting of genus g curves with g nodes on the K3 of the dual F-theory side. We present closed expressions for world-sheet tau-integrals with an arbitrary number of lattice vector insertions. Furthermore we verify that the corresponding heterotic one-loop couplings sum up perturbative open string and non-perturbative D-string contributions on the type I side. Finally we discuss a type I one-loop correction to the R^2 term.

26 pages, harvmac; Appendix about regularization included; Final version to appear in NPB

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• Heterotic/Type-I Duality in D<10 Dimensions, Threshold Corrections and D-Instantons
• Type IIB $R^4{H}^{4g-4}$ Conjectures
• D-strings in unconventional type I vacuum configurations
• Bound States of Type I D-Strings
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• Duality from Topological Symmetry
• Regularization of Automorphic Functions of Manifolds with Special Kähler Geometry

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