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Unformatted text preview: 1 EXTRA DIMENSIONS Updated Sept. 2007 by G.F. Giudice (CERN) and J.D. Wells (MCTP/Michigan). I Introduction The idea of using extra spatial dimensions to unify dif- ferent forces started in 1914 with Nordst om, who proposed a 5-dimensional vector theory to simultaneously describe elec- tromagnetism and a scalar version of gravity. After the in- vention of general relativity, in 1919 Kaluza noticed that the 5-dimensional generalization of Einstein theory can simultane- ously describe gravitational and electromagnetic interactions. The role of gauge invariance and the physical meaning of the compactification of extra dimensions was elucidated by Klein. However, the Kaluza-Klein (KK) theory failed in its original purpose because of internal inconsistencies and was essentially abandoned until the advent of supergravity in the late 1970s. Higher-dimensional theories were reintroduced in physics to ex- ploit the special properties that supergravity and superstring theories possess for particular values of spacetime dimensions. More recently it was realized [1,2] that extra dimensions with a fundamental scale of order TeV 1 could address the M W M Pl hierarchy problem and therefore have direct implications for collider experiments. Here we will review  the proposed scenarios with experimentally accessible extra dimensions. II Gravity in Flat Extra Dimensions II.1 Theoretical Setup Following Ref. 1, let us consider a D-dimensional spacetime with D = 4 + , where is the number of extra spatial dimensions. The space is factorized into R 4 M (meaning that the 4-dimensional part of the metric does not depend on extra- dimensional coordinates), where M is a -dimensional compact space with finite volume V . For concreteness, we will consider a -dimensional torus of radius R , for which V = (2 R ) . Standard Model (SM) fields are assumed to be localized on a (3 + 1)-dimensional subspace. This assumption can be realized in field theory, but it is most natural  in the setting of string theory, where gauge and matter fields can be confined to CITATION: K. Nakamura et al. (Particle Data Group), JPG 37 , 075021 (2010) (URL: http://pdg.lbl.gov) July 30, 2010 14:34 2 live on branes (for a review see Ref. 5). On the other hand, gravity, which according to general relativity is described by the spacetime geometry, extends to all D dimensions. The Einstein action takes the form S E = M 2+ D 2 Z d 4 x d y p det g R ( g ) , (1) where x and y describe ordinary and extra coordinates, re- spectively. The metric g , the scalar curvature R , and the re- duced Planck mass M D refer to the D-dimensional theory. The effective action for the 4-dimensional graviton is obtained by restricting the metric indices to 4 dimensions and by performing the integral in y . Because of the above-mentioned factorization hypothesis, the integral in y reduces to the volume V , and therefore the 4-dimensional reduced Planck mass is given by...
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This note was uploaded on 06/07/2011 for the course PHYS 4132 taught by Professor Kutter during the Spring '11 term at University of Florida.
- Spring '11