(Re)constructing Dimensions
Abstract
Compactifying a higherdimensional theory defined in R^1,3+n on an ndimensional manifold l M results in a spectrum of fourdimensional (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 KaluzaKlein 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 KaluzaKlein mass spectrum). Some of these examples are Ricciflat, 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 KaluzaKlein modes.
 Publication:

APS April Meeting Abstracts
 Pub Date:
 April 2003
 Bibcode:
 2003APS..APRK14009S