# Higher derivatives in Type II and M-theory on Calabi-Yau threefolds

## TL;DR

This paper derives four- and five-dimensional effective actions from Calabi-Yau threefold compactifications in string and M-theory, focusing on higher-derivative corrections and their impact on background solutions and fluctuations.

## Contribution

It provides a detailed derivation of higher-derivative terms in effective actions, including corrections from ten- and eleven-dimensional supergravity, and analyzes their effects on moduli fluctuations.

## Key findings

- Higher-derivative gravity terms are crucial for consistent effective actions.
- Additional higher-derivative form-field terms are necessary for correct supergravity form.
- Complete analysis for one-Kahler modulus case in Type II and M-theory.

## Abstract

The four- and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten- and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kahler structure of the compact space and the form-field background are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten- and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kahler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kahler modulus case is presented for both Type II theories and M-theory.