One-modulus Calabi-Yau fourfold reductions with higher-derivative terms

TL;DR

This paper studies M-theory compactified on warped Calabi-Yau fourfolds with higher-derivative corrections, analyzing their effects on the effective three-dimensional theory, especially the no-scale property and potential one-loop interpretations.

Contribution

It provides the first detailed reduction including eight-derivative terms, explores their impact on the Kahler potential, and constrains new higher-derivative terms for Calabi-Yau fourfolds.

Findings

Higher-derivative corrections break the no-scale condition.

Logarithmic corrections suggest a one-loop interpretation.

Additional eight-derivative terms can restore the no-scale property.

Abstract

In this note we consider M-theory compactified on a warped Calabi-Yau fourfold including the eight-derivative terms in the eleven-dimensional action known in the literature. We dimensionally reduce this theory on geometries with one Kahler modulus and determine the resulting three-dimensional Kahler potential and complex coordinate. The logarithmic form of the corrections suggests that they might admit a physical interpretation in terms of one-loop corrections to the effective action. Including only the known terms the no-scale condition in three dimensions is broken, but we discuss caveats to this conclusion. In particular, we consider additional new eight-derivative terms in eleven dimensions and show that they are strongly constrained by compatibility with the Calabi-Yau threefold reduction. We examine their impact on the Calabi-Yau fourfold reduction and the restoration of the no-scale property.