Gradient Formula for Linearly Self-Interacting Branes |
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Authors: | Brandon Carter Richard A Battye Jean–Philippe Uzan |
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Institution: | (1) LUTH, Bat. 18, Observatoire de Paris, 92195 Meudon, France, FR;(2) Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DL, U.K., GB;(3) Department of Physics and Astronomy, University of Manchester, Schuster Laboratory, Brunswick St, Manchester M13 9PL, U.K., GB;(4) Laboratoire de Physique Théorique, CNRS–UMR 8627, Bat. 210, Université Paris XI, 91405 Orsay Cedex, France, FR |
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Abstract: | The computation of long range linear self-interaction forces in string and higher dimensional brane models requires the evaluation
of the gradients of regularised values of divergent self-interaction potentials. It is shown that the appropriately regularised
gradient in directions orthogonal to the brane surface will always be obtainable simply by multiplying the regularised potential
components by just half the trace of the second fundamental tensor, except in the hypermembrane case for which the method
fails. Whatever the dimension of the background this result is valid provided the codimension is two (the hyperstring case)
or more, so it can be used for investigating brane-world scenarios with more than one extra space dimension.
Received: 15 April 2002 / Accepted: 23 October 2002 Published online: 25 February 2003
Communicated by H. Nicolai |
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