Comments on the four-dimensional effective theory for warped compactification

TL;DR

This paper derives four-dimensional effective theories from higher-dimensional supergravity models, revealing a broader solution space including cosmological solutions with shrinking internal dimensions, which are not present in the original theories.

Contribution

It demonstrates that effective four-dimensional theories can admit solutions not possible in the higher-dimensional origins, highlighting caution in their use.

Findings

Effective theories allow a wider class of solutions.

Cosmological solutions with decreasing internal space size.

Higher-dimensional theories do not permit these solutions.

Abstract

We derive four-dimensional effective theories for warped compactification of the ten-dimensional IIB supergravity and the eleven-dimensional Horava-Witten model. We show that these effective theories allow a much wider class of solutions than the original higher-dimensional theories. In particular, the effective theories have cosmological solutions in which the size of the internal space decreases with the cosmic expansion in the Einstein frame. This type of compactifying solutions are not allowed in the original higher-dimensional theories. This result indicates that the effective four-dimensional theories should be used with caution, if one regards the higher-dimensional theories more fundamental.