DUALITY IN SUPERSTRING COMPACTIFICATIONS WITH MAGNETIC-FIELD BACKGROUNDS

Motivated by the work of Polchinski and Strominger on type IIA theory, where the effect of non-trivial held strengths for p-form potentials on a Calabi-Yau space was discussed, we study four-dimensional heterot ic string theory in the presence of a magnetic field on a 2-cycle in t he internal manifold, for both N = 4 and N = 2 cases. We show that at special points in the moduli space certain perturbative charged states become tachyonic and stabilize the vacuum by acquiring vacuum expecta tion values, thereby restoring supersymmetry. We discuss both the case s where the tachyons appear with a tower of Landau levels, which becom e light in the limit of large volume of the 2-cycle, and the case wher e such Landau levels are not present. In the latter case it is suffici ent to restrict the analysis to the quartic potential for the tachyon, On the other hand, in the former case it is necessary to include the Landau levels in the analysis of the potential; for toroidal and orbif old examples, we give an explicit CFT description of the new supersymm etric vacuum, The resulting new vacuum turns out to be in the same cla ss as the original supersymmetric one, Finally, using duality, we disc uss the role of the Landau levels on the type IIA side. (C) 1998 Elsev ier Science B.V.