Heterotic M-theory in Five Dimensions

TL;DR

This work derives the complete five-dimensional effective action for the (1,1) sector of strongly coupled heterotic M-theory by reducing M-theory on a Calabi–Yau threefold with an S^1/Z_2 orbifold, keeping a nonzero internal G_4 mode that sources boundary fields. The resulting bulk theory is a gauged D=5, N=1 supergravity with h^{1,1}-1 vector multiplets and a universal hypermultiplet, coupled to boundary E_6 and E_8 theories, with bulk and boundary potentials controlled by five-brane charges α_i. A multi-charged BPS domain-wall (three-brane) solution is constructed, providing a natural vacuum around which to formulate four-dimensional phenomenology and cosmology; reducing on this domain wall yields a 4D N=1 theory with explicit α_i-dependent corrections to the Kaehler potential and gauge kinetic functions. The paper thus connects the 11D Hořava–Witten setup to a concrete 4D effective theory, clarifying the role of nonzero G_4 modes and gauging in generating potentials and consistent domain-wall vacua with potential phenomenological relevance, including controlled gaugino-condensation contributions.

Abstract

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 Kahler potential and threshold corrections to the gauge kinetic functions.