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 \( \mathcal{N}=2 \) 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.
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Andriot, D., Tsimpis, D. Laplacian spectrum on a nilmanifold, truncations and effective theories. J. High Energ. Phys. 2018, 96 (2018). https://doi.org/10.1007/JHEP09(2018)096
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DOI: https://doi.org/10.1007/JHEP09(2018)096