2018/06/30 by David Andriot, Dimitrios Tsimpis
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Compactification (mathematics) #Connection (principal bundle) #Continuous spectrum #Dimensional reduction #Energy spectrum #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Laplace operator #Limit (mathematics) #Operator (biology) #Spectrum (functional analysis) #hep-ph #hep-th #math.SP
paper · pdf · doi:10.1007/jhep09(2018)096
v2: minor modifications, published version
openalex created_date 2018/06/21 · openalex publication_date 2018/09/01 · arxiv created 2018/10/11 · arxiv updated 2018/10/17 · openalex updated_date 2026/08/05
A bstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> 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.