  We study heterotic vacua with four supercharges in three and four space-time
dimensions and their duals obtained as M/F-theory compactified on Calabi-Yau
fourfolds. We focus on their respective moduli spaces and derive the Kahler
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.
