EIKONAL PARTICLE SCATTERING AND DILATON GRAVITY

Approximating light charged pointlike particles in terms of (nonextrem al) dilatonic black holes is shown to lead to certain pathologies in P lanckian scattering in the eikonal approximation, which are traced to the presence of a (naked) curvature singularity in the metric of these black holes. The existence of such pathologies is confirmed by analyz ing the problem in an ''external metric'' formulation where an ultrare lativistic point particle scatters off a dilatonic black hole geometry at large impact parameters. The maladies disappear almost trivially u pon imposing the extremal limit. Attempts to derive an effective three -dimensional ''boundary'' field theory in the eikonal limit are stymie d by four-dimensional (bulk) terms proportional to the light-cone deri vatives of the dilaton field, leading to nontrivial mixing of electrom agnetic and gravitational effects, in contrast with the case of genera l relativity. An eikonal scattering amplitude, showing decoupling of t hese effects, is shown to be derivable by resummation of graviton, dil aton, and photon exchange ladder diagrams in a linearized version of t he theory for an asymptotic value of the dilaton field which makes the string coupling constant nonperturbative.