Laplacian spectrum on a nilmanifold, truncations and effective theories

Abstract

Motivated by low energy effective theories arising from compactification on curved manifolds, we determine the complete spectrum of the Laplacian operator on the three-dimensional Heisenberg nilmanifold. We first use the result to construct a finite set of forms leading to an N=2 gauged supergravity, upon reduction on manifolds with SU(3) structure. Secondly, we show that in a certain geometrical limit the spectrum is truncated to the light modes, which turn out to be left-invariant forms of the nilmanifold. We also study the behavior of the towers of modes at different points in field space, in connection with the refined swampland distance conjecture.

arXiv commentv2: minor modifications, published version

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• Tachyonic de Sitter solutions of 10d type II supergravities
• Kaluza-Klein spectrometry for $\mathrm{Ad}{\mathrm{S}}_3$ vacua
• Gravitational waves in warped compactifications
• Warp factor and the gravitational wave spectrum
• Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation
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• A new mechanism for symmetry breaking from nilmanifolds
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Consistent truncation with dilatino condensation on nearly Kähler and Calabi-Yau manifolds