4D Superfield Reduction of 5D Orbifold SUGRA and Heterotic M-theory

TL;DR

This paper develops a superfield formalism to reduce 5D supergravity on an S^1/Z_2 orbifold to 4D, covering various models including heterotic M-theory, and analyzes the resulting effective actions and moduli stabilization.

Contribution

It introduces a unified superfield approach to 5D supergravity reduction, enabling explicit derivation of 4D effective actions for diverse models including heterotic M-theory.

Findings

Derived 4D Kaehler potentials and superpotentials for unwarped geometries.

Provided a master formula for the Kaehler potential in RS-like models.

Formulated the superfield description of 5D heterotic M-theory with 5-branes.

Abstract

We present a detailed study of the reduction to 4D of 5D supergravity compactified on the S^1/Z_2 orbifold. For this purpose we develop and employ a recently proposed N=1 conformal superfield description of the 5D supergravity couplings to abelian vector and hypermultiplets. In particular, we obtain a unique relation of the "radion" to chiral superfields as in global 5D SUSY and we can embed the universal hypermultiplet into this formalism. In our approach, it is transparent how the superconformal structure of the effective 4D actions is inherited from the one of the original 5D supergravity. We consider both ungauged and gauged 5D supergravities. This includes compactifications in unwarped geometries, generalizations of the supersymmetric Randall-Sundrum (RS) model as well as 5D heterotic M-theory. In the unwarped case, after obtaining the effective Kaehler potentials and superpotentials, we demonstrate that the tree-level 4D potentials have flat and/or tachyonic directions. One-loop corrections to the Kaehler potential and gaugino condensation are presented as suitable tools for moduli stabilization to be discussed in subsequent work. Turning to the RS-like models, we obtain a master formula for the Kaehler potential for an arbitrary number of vector and hyper moduli, which we evaluate exactly for special cases. Finally, we formulate the superfield description of 5D heterotic M-theory and obtain its effective 4D description for the universal (h^(1,1)=1) case, in the presence of an arbitrary number of bulk 5-branes. We present, as a check of our expressions, time-dependent solutions of 4D heterotic M-theory, which uplift to 5D solutions generalizing the ones recently found in hep-th/0502077.