Heterotic M-theory in Five Dimensions

TL;DR

This paper derives the five-dimensional effective action of heterotic M-theory on a Calabi-Yau, revealing a gauged supergravity with potential terms, and constructs a BPS domain wall solution relevant for phenomenology and cosmology.

Contribution

It provides the complete five-dimensional effective theory including non-zero modes and constructs a BPS domain wall solution, advancing understanding of heterotic M-theory compactifications.

Findings

Derived the 5D effective action with non-zero modes.

Constructed a multi-charged BPS domain wall solution.

Calculated corrections to the 4D supergravity matter Kahler potential.

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.