FINITENESS AND UNITARITY OF LORENTZ-COVARIANT GREEN-SCHWARZ SUPERSTRING AMPLITUDES

In two recent papers, a new method was developed for calculating ten-dimensional superstring amplitudes with an arbitrary number of loops and external massless bosons or fermions, and for expressing the amplitudes in manifestly Lorentz-invariant form. In this paper, all amplitudes with external massless bosons are proven to be finite by explicitly checking for divergences when the Riemann surface degenerates. These amplitudes are then proven to be unitary by choosing light-cone moduli for the surface and comparing with the light-cone Green-Schwarz formalism.