THE BOX GRAPH IN SUPERSTRING THEORY

In theories of closed oriented superstrings, the one-loop amplitude is given by a single diagram, with the topology of a torus. Its interpre tation had remained obscure, because it was formally real, converged o nly for purely imaginary values of the Mandelstam variables, and had t o account for the singularities of both the box graph and the one-part icle reducible graphs in field theories. We present in detail an analy tic continuation method which resolves all these difficulties. It is b ased 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 formal ly to an infinite superposition of box graphs in phi(3)-like field the ories, whose divergence is responsible for the poles in the string amp litudes. This paper is a considerable simplification and generalizatio n of our earlier proposal published in Phys. Rev. Lett. 70 (1993) 3692 .