Universe as a domain wall

TLDR

The authors construct the theory via generalized dimensional reduction on a Calabi‑Yau manifold, retaining a non‑zero mode of the four‑form field strength that gauges the universal hypermultiplet, and obtain a background of two parallel three‑branes whose worldvolume defines four‑dimensional spacetime. The effective five‑dimensional theory of the strongly coupled heterotic string is a gauged N=1 supergravity with four‑dimensional boundaries, and it admits an exact three‑brane domain wall solution that linearizes to Witten’s deformed Calabi‑Yau background.

Abstract

It is shown that the effective five-dimensional theory of the strongly coupled heterotic string is a gauged version of N=1 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 four-dimensional boundary theories and constitutes the appropriate background for a reduction to four dimensions. Four-dimensional space-time is then identified with the three-brane worldvolume.