High-energy unitarity of gravitation and strings

It is known that the behavior of a four-point string amplitude at large center-of-mass energy ..sqrt..s and fixed momentum transfer q = ..sqrt..-t is not perturbative. We study this region of phase space by summing multiple Reggeized graviton exchange in the eikonal approximation in D space-time dimensions. It is argued that the eikonal sum is at least representative of the summation of the leading powers of s in a string theory. The masslessness and high spin of the (Reggeized) graviton determine the character of the result. For kappa/sup 2/sq/sup D-4/approx. >1 is quite nonperturbative in character: simple Regge behavior and the Froissart bound are violated, and the amplitude does not satisfy a fixed-momentum-transfer dispersion relation. Although order by order the amplitude exhibits in q/sup 2/ the exponential decrease of Regge behavior, the final amplitude has only power-law falloff dependent on the number of space-time dimensions but independent of the Regge slope. The unitarity of the partial-wave projections of the eikonal amplitude is also studied. It is demonstrated that for Dgreater than or equal to4 noncompact dimensions, the partial-wave amplitudes are bounded as s..-->..infinity only for large values of angular momentum, lapprox. >x/sub 0/ ..sqrt..s , where x/sub 0/ is the dominant value of the impact parameter.