Higher derivative couplings and heterotic-type I duality in eight dimensions

We calculate F-4 and (RT4g-4)-T-4 couplings in d = 8 heterotic and type I s tring vacua (with gauge and graviphoton field strengths F,T, and Riemann cu rvature R). The holomorphic piece F-g of the heterotic one-loop coupling (R T4g-4)-T-4 is given by a polylogarithm of index 5 - 4g and encodes the coun ting 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 corres ponding heterotic one-loop couplings sum up perturbative open string and no n-perturbative D-string contributions on the type I side. Finally we discus s a type I one-loop correction to the R-2 term. (C) 1999 Elsevier Science B .V. All rights reserved.