  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.
