document: In this section we wish to calculate the cross section for the absorption of massless scalars by the self-dual string in the world volume of the M-theory five-brane. We will adopt an entirely world volume approach similar to that of [21–23]. We begin by writing the equation satisfied by the s-wave with energy ω, φ(r,t)=φ(r)eiωt, of the linear fluctuations of the four overall transverse scalars about the self-dual string, (it is known that there are problems when one considers higher angular momentum modes [23], one must take care with the validity of the linearized approximation, this is discussed in [13]): (15)ρ−3ddρρ3ddρ+1+R6ω6ρ6φ(ρ)=0, where ρ=rω, R=Q1/3ℓp. Note, as pointed out by [11] world volume solitons have a much sharper potential than the Coulomb type potential typical of brane solutions in supergravity; thus this scattering is different to that of the string in six-dimensional supergravity. Nevertheless, for small ωR one may solve this problem by matching an approximate solution in the inner region to an approximate solution in the outer region; this follows closely the supergravity calculation [24].
doc_bio_tags: O O O O O O B I I I I I I I I I O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O B I O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O B I O O O O O O O O B I O
extractive_keyphrases: approximate solution brane solutions calculate the cross section for the absorption of massless scalars entirely world volume approach higher angular momentum modes linear fluctuations linearized approximation small ωr supergravity calculation world volume solitons
abstractive_keyphrases: massless scalars m-theory five-brane self-dual string s-wave