(Re)constructing Dimensions
arXiv:hep-th/0212144 · doi:10.1088/1126-6708/2003/05/045
Abstract
Compactifying a higher-dimensional theory defined in R^{1,3+n} on an n-dimensional manifold {\cal M} results in a spectrum of four-dimensional (bosonic) fields with masses m^2_i = λ_i, where - λ_i are the eigenvalues of the Laplacian on the compact manifold. The question we address in this paper is the inverse: given the masses of the Kaluza-Klein fields in four dimensions, what can we say about the size and shape (i.e. the topology and the metric) of the compact manifold? We present some examples of isospectral manifolds (i.e., different manifolds which give rise to the same Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and Kähler and so they are isospectral backgrounds for string theory. Utilizing results from finite spectral geometry, we also discuss the accuracy of reconstructing the properties of the compact manifold (e.g., its dimension, volume, and curvature etc) from measuring the masses of only a finite number of Kaluza-Klein modes.
23 pages, 3 figures, 2 references added
References in corpus (6)
- (De)Constructing Dimensions
- Chiral Four-Dimensional N=1 Supersymmetric Type IIA Orientifolds from Intersecting D6-Branes
- Three-Family Supersymmetric Standard-like Models from Intersecting Brane Worlds
- Gauge Invariant Effective Lagrangian for Kaluza-Klein Modes
- Type I Strings with F- and B-Flux
- Shadows of the Planck Scale: The Changing Face of Compactification Geometry