Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-10-20
Nucl.Phys.B440:24-94,1995
Physics
High Energy Physics
High Energy Physics - Theory
Plain TeX, 67 pp. and 9 figures, Columbia/UCLA/94/TEP/39
Scientific paper
10.1016/0550-3213(94)00526-K
In theories of closed oriented superstrings, the one loop amplitude is given by a single diagram, with the topology of a torus. Its interpretation had remained obscure, because it was formally real, converged only for purely imaginary values of the Mandelstam variables, and had to account for the singularities of both the box graph and the one particle reducible graphs in field theories. We present in detail an analytic continuation method which resolves all these difficulties. It is based on a reduction to certain minimal amplitudes which can themselves be expressed in terms of double and single dispersion relations, with explicit spectral densities. The minimal amplitudes correspond formally to an infinite superposition of box graphs on $\phi ^3$ like field theories, whose divergence is responsible for the poles in the string amplitudes. This paper is a considerable simplification and generalization of our earlier proposal published in Phys. Rev. Lett. 70 (1993) p 3692.
D'Hoker Eric
Phong Duong Hong
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