4-GRAVITON SCATTERING IN D = 4 SUPERSTRINGS WITH BROKEN SPACE-TIME SUPERSYMMETRY

We construct the one-loop four-graviton amplitude in a four-dimensional type II superstring model with broken (N = 4) space-time SUSY. The amplitude is seen to be a sum of the amplitude with unbroken highest N = 8 SUSY, A8, plus a term A4 which breaks SUSY down to N = 4. The new term A4 is seen to contain rescattering diagrams, which are also present in A8, and to open one-particle-reducible channels containing gravitons, due to the absence of non-renormalization theorems for it. The evaluation of the contributions to the amplitude of these channels in the limit of large external energies and of small momentum transfer confirms that the effective metric due to a graviton source is not of the classical Schwarzschild-type, not even at broken SUSY. Moreover, we check that, in spite of the absence of non-renormalization theorems, the graviton mass and wave function are not renormalized. We find infrared singularities in A4, which are not present in A8, individuate their nature and guess a ...