On M-theory fourfold vacua with higher curvature terms

TL;DR

This work analyzes M-theory compactifications on eight-dimensional manifolds with higher-derivative corrections, showing the internal space remains conformally Kahler with vanishing first Chern class but the metric becomes non-Ricci-flat due to non-harmonic third Chern form contributions. By expanding the fields in α and solving the modified Einstein and Chern–Simons equations, the authors obtain an explicit α^2-corrected internal metric with a warp factor and a harmonic G^(1) flux, linking these to topological data X_8 and Z. They derive Killing spinor equations at order α^2 and translate them into differential constraints on globally defined forms J and Ω, revealing that the internal geometry is still an SU(4) structure manifold with a nontrivial, exact W5 torsion class and a deformed holomorphic form. The results provide a concrete, geometrically controlled framework for analyzing supersymmetry in warped Calabi–Yau fourfold compactifications with higher-curvature terms, while leaving open the complete form of the gravitino variation and a full 3D effective action.

Abstract

We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kahler manifold with vanishing first Chern class. The metric solution, however, is non-Ricci-flat even when allowing for a conformal rescaling including the warp factor. This deviation is due to the possible non-harmonicity of the third Chern-form in the leading order Ricci-flat metric. We present a systematic derivation of the background solution by solving the Killing spinor conditions including higher curvature terms. These are translated into first-order differential equations for a globally defined real two-form and complex four-form on the fourfold. We comment on the supersymmetry properties of the described solutions.