High energy scattering amplitudes in matrix string theory

Abstract

High energy fixed angle scattering is studied in matrix string theory. The saddle point world sheet configurations, which give the dominant contributions to the string theory amplitude, are taken as classical backgrounds in matrix string theory. A one loop fluctuation analysis about the classical background is performed. An exact treatment of the fermionic and bosonic zero modes is shown to lead to all of the expected structure of the scattering amplitude. The ten dimensional Lorentz invariant kinematical structure is obtained from the fermion zero modes, and the correct factor of the string coupling constant is obtained from the abelian gauge field zero modes. Up to a numerical factor we reproduce, from matrix string theory, the high energy limit of the tree level, four graviton scattering amplitude.

harvmac.tex, 55 pages, typos corrected, includes 2 figures. First part of section 3 expanded to give a clearer discussion of the justification for using a one loop calculation. Two paragraphs added to the end of section 8.1 discussing the non-Lorentz invariant factor $c$ equn 8.9. It is pointed out that the same factor occurs in string theory where it combines with the determinant to give a Lorentz Invaraint result. Other minor changes. Final version to appear in Nucl. Phys B