Spacetime as a membrane in higher dimensions

By G. W. Gibbons, D. Wiltshire. 2001

263 citations recorded by the source corpus.

By means of a simple model we investigate the possibility that spacetime is a membrane embedded in higher dimensions. We present cosmological solutions of d-dimensional Einstein-Maxwell theory which compactify to two dimensions. These solutions are analytically continued to obtain dual solutions in which a (d − 2)-dimensional Einstein spacetime “membrane” is embedded in d dimensions. The membrane solutions generalise Melvin's 4-dimensional flux tube solution. The flat membrane is shown to be classically stable. It is shown that there are zero mode solutions of the d-dimensional Dirac equation which are confined to a neighbourhood of the membrane and move within it like massless chiral (d − 2)-dimensional fermions. An investigation of the spectrum of scalar perturbations shows that a well-defined mass gap between the zero modes and massive modes can be obtained if there is a positive cosmological term in (d − 2) dimensions or a negative cosmological term in d dimensions.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5486e38c6403a07704c44c6ce926478891cfe022

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Citations in the corpus

S brane solutions in supergravity theories (2002, background): “Furthermore given the relation of brane antibrane systems to fluxbranes [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], it might be possible that the time dependent solutions describe the dynamical evolution of fluxbranes.”
A New cosmological scenario in string theory (2002, background): “–De Sitter space but retains the standard properties of higher dimensional black holes. A short cut to construct such generalization is to realize the similarity between the dilatonic Melvin solution [26] and the cosmological solution of section 2. In the case of the Kalu z˙a–Klein Melvin solution, ”
D‐branes in Standard Model building, gravity and cosmology (2003, background): “in the required range of distances. There are three such mechanisms known as explained earlier: (1) The internal space is non-compact with its Laplacian having a suﬃciently large gap above zero [273]-[275]. (2) The internal space is non-compact with a gap-less Laplacian with an appropriate density o”
Brane-World Gravity (2004, methodology): “They were preceded by the Arkani–Hamed–Dimopoulos–Dvali (ADD) brane-world models [15, 14, 13, 6, 367, 421, 168, 173], which put forward the idea that a large volume for the compact extra dimensions would lower the fundamental Planck scale, Mew ∼ 1 TeV .”
Cosmological evolution of the rolling tachyon (2002, background): “Because the theories are formulated in higher dimensions, one must either construct a spontaneous compactification scenario or imagine a scheme in which the universe is sort of 3-brane [3].”