A ten-dimensional super-Poincare covariant formalism for the superstring was
recently developed which involves a BRST operator constructed from superspace
matter variables and a pure spinor ghost variable. A super-Poincare covariant
prescription was defined for computing tree amplitudes and was shown to
coincide with the standard RNS prescription.
In this paper, picture-changing operators are used to define functional
integration over the pure spinor ghosts and to construct a suitable b ghost.
A super-Poincare covariant prescription is then given for the computation of
N-point multiloop amplitudes. One can easily prove that massless N-point
multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of
superstring theory. One can also prove the Type IIB S-duality conjecture that
R4 terms in the effective action receive no perturbative contributions above
one loop.Comment: 45 pages harvmac tex, added minor clarification