Some superstring amplitude computations with the non-minimal pure spinor formalism

We use the non-minimal pure spinor formalism to compute in a super-Poincarecovariant manner the four-point massless one and two-loop open superstringamplitudes, and the gauge anomaly of the six-point one-loop amplitude. All ofthese amplitudes are expressed as integrals of ten-dimensional superfields in a"pure spinor superspace" which involves five $\theta$ coordinates covariantlycontracted with three pure spinors. The bosonic contribution to theseamplitudes agrees with the standard results, and we demonstrate identitieswhich show how the $t_8$ and $\epsilon_{10}$ tensors naturally emerge fromintegrals over pure spinor superspace.Comment: 20 pages, harvmac te