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It is shown that the effective five-dimensional theory of the strongly coupled heterotic string is a gauged version of Nϭ1 five-dimensional supergravity with four-dimensional boundaries. For the universal supermultiplets, this theory is explicitly constructed by a generalized dimensional reduction procedure on a Calabi-Yau manifold. A crucial ingredient in the reduction is the retention of a ''non-zero mode'' of the four-form field strength, leading to the gauging of the universal hypermultiplet by the graviphoton. We show that this theory has an exact three-brane domain wall solution which reduces to Witten's ''deformed'' Calabi-Yau background upon linearization. This solution consists of two parallel three-branes with sources provided by the fourdimensional boundary theories and constitutes the appropriate background for a reduction to four dimensions. Four-dimensional space-time is then identified with the three-brane world volume. ͓S0556-2821͑98͒02122-5͔

We derive the five-dimensional effective action of strongly coupled heterotic string theory for the complete (1, 1) sector of the theory by performing a reduction, on a Calabi-Yau three-fold, of M-theory on S 1 /Z 2 . A crucial ingredient for a consistent truncation is a non-zero mode of the antisymmetric tensor field strength which arises due to magnetic sources on the orbifold planes.The correct effective theory is a gauged version of five-dimensional N = 1 supergravity coupled to Abelian vector multiplets, the universal hypermultiplet and four-dimensional boundary theories with gauge and gauge matter fields. The gauging is such that the dual of the four-form field strength in the universal multiplet is charged under a particular linear combination of the Abelian vector fields. In addition, the theory has potential terms for the moduli in the bulk as well as on the boundary. Because of these potential terms, the supersymmetric ground state of the theory is a multi-charged BPS three-brane domain wall, which we construct in general. We show that the five-dimensional theory together with this solution provides the correct starting point for particle phenomenology as well as early universe cosmology. As an application, we compute the four-dimensional N = 1 supergravity theory for the complete (1, 1) sector to leading nontrivial order by a reduction on the domain wall background. We find a correction to the matter field Kähler potential and threshold corrections to the gauge kinetic functions.