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

Thomas W. Grimm, Tom G. Pugh, Matthias Weissenbacher

TL;DR

This work derives a three-dimensional N=2 effective action from eleven-dimensional supergravity with higher-derivative corrections on warped Calabi–Yau fourfolds with fluxes. It shows that the scalar potential is purely flux-induced, with backreaction from the warp factor canceling naive higher-curvature contributions, and demonstrates consistency with 3D N=2 supersymmetry and no-scale structure. The authors construct the Kähler potential and complex coordinates as a δv expansion and propose divisor-integral definitions T_i to capture warp and higher-derivative effects, revealing a deep interplay between warping and higher-curvature terms and suggesting higher-derivative corrections to the M5-brane action. The results establish a framework for further higher-order reductions and potential F-theory uplifts, highlighting semi-topological divisor data and non-harmonic c_4 contributions as key elements of the moduli dynamics.

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 Kähler 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 Kähler 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.

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

TL;DR

This work derives a three-dimensional N=2 effective action from eleven-dimensional supergravity with higher-derivative corrections on warped Calabi–Yau fourfolds with fluxes. It shows that the scalar potential is purely flux-induced, with backreaction from the warp factor canceling naive higher-curvature contributions, and demonstrates consistency with 3D N=2 supersymmetry and no-scale structure. The authors construct the Kähler potential and complex coordinates as a δv expansion and propose divisor-integral definitions T_i to capture warp and higher-derivative effects, revealing a deep interplay between warping and higher-curvature terms and suggesting higher-derivative corrections to the M5-brane action. The results establish a framework for further higher-order reductions and potential F-theory uplifts, highlighting semi-topological divisor data and non-harmonic c_4 contributions as key elements of the moduli dynamics.

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 Kähler 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 Kähler 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.

Paper Structure

This paper contains 12 sections, 53 equations.

Table of Contents

  1. Introduction
  2. Dimensional reduction of the M-theory action
  3. Higher-order background solution
  4. Considered variations of the background solution
  5. Scalar potential
  6. Three-dimensional effective action
  7. Warp-factor scaling symmetry and integration
  8. Demonstrating the supersymmetric structure
  9. Comparing the reduction result with $\mathcal{N}=2$ supergravity
  10. Kähler potential and coordinates as a $\delta v$ expansion
  11. Completing the Kähler potential and complex coordinates
  12. Conclusions