Type IIA and heterotic string vacua in D=2

We study type IIA string theory compactified on Calabi-Yau fourfolds and he terotic string theory compactified on Calabi-Yau threefolds times a two-tor us. We derive the resulting effective theories which have two spacetime dim ensions and preserve four supercharges. The duality between such vacua is e stablished at the level of the effective theory. For type IIA vacua with no n-trivial Ramond-Ramond background fluxes a superpotential is generated, We show that for a specific choice of background fluxes and a fourfold which has the structure of a threefold fibred over a sphere the superpotential co incides with the superpotential recently proposed by Taylor and Vafa in com pactifications of type IIB string theory on a threefold. (C) 2001 Elsevier Science B.V. All rights reserved.