High-energy unitarity of gravitation and strings

Details High-energy unitarity of gravitation and strings High-energy unitarity of gravitation and strings

Jan 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrvd..37..359m&link_type=abstract

Physical Review D (Particles and Fields), Volume 37, Issue 2, 15 January 1988, pp.359-367

Physics

81

Partial-Wave Analysis, Approximations

Scientific paper

It is known that the behavior of a four-point string amplitude at large center-of-mass energy √s and fixed momentum transfer q= √-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 κ2sqD-4<~1 (κ is the gravitational coupling), the eikonal amplitude is dominated by single Reggeized graviton exchange. The amplitude in the region κ2sqD-4>>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 q2 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 D>=4 noncompact dimensions, the partial-wave amplitudes are bounded as s-->∞ only for large values of angular momentum, l>~x0 √s , where x0 is the dominant value of the impact parameter. A heuristic argument is presented that the eikonal approximation is successful in unitarizing Reggeized graviton exchange as t/s-->0 in four dimensions but not in higher dimensions.

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