Raúl Rabadán and Gary Shiu JHEP05(2003)045 doi:10.1088/1126-6708/2003/05/045
(Re)constructing dimensions
Raúl Rabadán1 and Gary Shiu2
Show affiliationsCompactifying a higher-dimensional theory defined in 
1,3+n on an n-dimensional manifold 
results in a spectrum of four-dimensional (bosonic) fields with masses m2i = λi, where −λi 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.
- Keywords
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E-print Number: hep-th/0212144
Cited: by |
Refers: to
- PACS
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11.25.Mj Compactification and four-dimensional models
02.40.Ky Riemannian geometries
11.10.Jj Asymptotic problems and properties
04.50.-h Higher-dimensional gravity and other theories of gravity
- Subjects
- Dates
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Issue 05 (May 2003)
Received 16 January 2003, accepted for publication 19 May 2003
Published 27 May 2003
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(Re)constructing dimensions
Raúl Rabadán and Gary Shiu JHEP05(2003)045
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