PARTICLE TRANSMUTATION FROM THE SCATTERING OF STRINGS AND SUPERSTRINGS IN CURVED SPACE-TIME

We give a general formulation of the scattering of strings by a curved space-time geometry, for both open and closed bosonic strings and for supersymmetric ones. We assume that the space-time admits flat regions in order to define ingoing and outgoing states, and we analyze the particle content of the scattering. Due to the interaction with the geometry, we find inelastic processes in which the initial particle of mass m and spin s transmutes into a different final particle of mass m' and spin s'. We also find elastic processes in which initial and final states describe the same particle (although the momentum and the spin polarization may change). At first order in square-root-of alpha', for string oscillations small compared with the energy scales of the metric, outgoing and ingoing oscillator operators are related by a linear, or Bogoliubov transformation. We compute the more relevant transition amplitudes: from the ground state to a dilaton, to a graviton and to massive states; and the transmutation of a dilaton into a graviton. For supersymmetric strings, massless particles cannot transmute among themselves (this is true to all orders in square-root-alpha'). Several properties of the particle transmutation processes follow directly from the symmetry properties of the geometry. Explicit examples as black holes and gravitational shock-wave space-times are given.