The effective action of warped M-theory reductions with higher-derivative terms - Part II

TL;DR

This paper derives the three-dimensional effective action from warped M-theory reductions with higher-derivative terms, analyzing flux contributions, supersymmetry, and moduli space structure, including higher-derivative corrections to M5-branes.

Contribution

It provides a detailed analysis of the effective action including fluxes, warp-factors, and higher-curvature effects, clarifying the structure of the moduli space and supersymmetry compatibility.

Findings

Fluxes induce the potential, higher-curvature contributions vanish with back-reaction.

The Kähler potential and complex coordinates are compatible with N=2 supersymmetry.

Complex coordinates are expressed as divisor integrals, revealing interplay between warp-factor and higher-curvature terms.

Abstract

We study the three-dimensional effective action obtained by reducing eleven-dimensional supergravity with higher-derivative terms on a background solution including a warp-factor, an eight-dimensional compact manifold, and fluxes. The dynamical fields are K\"ahler deformations and vectors from the M-theory three-form. We show that the potential is only induced by fluxes and the naive contributions obtained from higher-curvature terms on a Calabi-Yau background vanish once the back-reaction to the full solution is taken into account. For the resulting three-dimensional action we analyse the K\"ahler potential and complex coordinates and show compatibility with N=2 supersymmetry. We argue that the higher-order result is also compatible with a no-scale condition. We find that the complex coordinates should be formulated as divisor integrals for which a non-trivial interplay between the warp-factor terms and the higher-curvature terms allow a derivation of the moduli space metric. This leads us to discuss higher-derivative corrections to the M5-brane action.