Physics Letters B (Apr 2015)

On M-theory fourfold vacua with higher curvature terms

  • Thomas W. Grimm,
  • Tom G. Pugh,
  • Matthias Weißenbacher

DOI
https://doi.org/10.1016/j.physletb.2015.02.047
Journal volume & issue
Vol. 743
pp. 284 – 289

Abstract

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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 Kähler 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.