On M-theory fourfold vacua with higher curvature terms

TL;DR

This paper investigates eleven-dimensional supergravity solutions with higher curvature corrections, revealing that the internal eight-dimensional space is conformally Kahler with specific geometric properties, and derives conditions for supersymmetry preservation.

Contribution

It provides a systematic derivation of M-theory fourfold solutions including higher curvature terms, highlighting the geometric structure and supersymmetry conditions.

Findings

Internal space is conformally Kahler with vanishing first Chern class.

The metric is non-Ricci-flat due to non-harmonicity of the third Chern-form.

Derived first-order differential equations for forms governing supersymmetry.

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.