Duality in heterotic vacua with four supercharges

We study heterotic vacua with four supercharges in three and four space-tim e dimensions and their duals obtained as M/F-theory compactified on Calabi- Yau fourfolds. We focus on their respective moduli spaces and derive the Ka hler potential for heterotic vacua obtained as circle compactifications of four-dimensional N = 1 heterotic theories. The Kahler potential of the dual theory is computed by compactifying 11-dimensional supergravity on Calabi- Yau fourfolds. The duality between these theories is checked for K3-fibred fourfolds and an appropriate F-theory limit is discussed. (C) 2000 Elsevier Science B.V. All rights reserved.