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

TL;DR

The paper develops a systematic framework to include higher-derivative corrections in Calabi–Yau threefold compactifications of Type II string theories and M-theory, deriving 4D and 5D effective actions with up to four space-time derivatives. Starting from known eight-derivative corrections in 10D/11D, it determines corrected backgrounds and analyzes fluctuations of Kahler structure and form fields, revealing that extra higher-derivative form-field terms are required for consistency with 4D/5D supersymmetry. It provides explicit reductions to 5D N=2 supergravity, detailing four-derivative couplings in the Kahler-moduli and vector sectors, and presents exact one-modulus results showing a Gauss–Bonnet gravity term plus a (∂u)^4 interaction after field redefinitions. The work also discusses duality between M-theory and Type II theories at this order, includes Type IIA/IIB differences, and comments on orientifold truncations and potential moduli-stabilization implications, highlighting remaining ambiguities and avenues for a complete higher-derivative N=1 formulation.

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.