Fluxes in heterotic and type II string compactifications

In this paper we consider heterotic compactifications on K3 x T-2 as well as type II compactifications on K3-fibred Calabi-Yau spaces with certain fluxes for the gauge and R-R field strengths F and H turned on. By providing an identification of corresponding fluxes we show that the well-known N = 2 heterotic/type 11 string-string duality still holds for a subset of all possible fluxes, namely those which arise from six-dimensional gauge fields with internal magnetic flux on the common two-sphere P-b(1), which is the base space of the type II K3-fibration. On the other hand, F- and H-fluxes without P-b(1)-support, such as heterotic F-fluxes on the torus T-2 or type 11 H-fluxes on cycles of the K3-fibre cannot be matched in any simple way, which is a challenge for heterotic/type II string-string duality. Our analysis is based on the comparison of terms in the effective low-energy heterotic and type II actions which are induced by the fluxes, such as the Green--Schwarz couplings related to flux-induced U(l) anomalies, the effective superpotential and the Fayet-Iliopoulos scalar potential. (C) 2002 Elsevier Science B.V. All rights reserved.