In this paper we present two (a priori independent) derivations of the eikonal operator in string-brane scattering. The first one is obtained by summing surfaces with any number of boundaries, while in the second one the eikonal operator is derived from the three-string vertex in a suitable light-cone gauge. This second derivation shows that the bosonic oscillators present in the leading eikonal operator are to be identified with the string bosonic oscillators in a suitable light-cone gauge, while the first one shows that it exponentiates recovering unitarity. This paper is a review of results obtained in two previous publications of the same authors.
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