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

Abstract

We use the non-minimal pure spinor formalism to compute in a super-Poincaré covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these amplitudes are expressed as integrals of ten-dimensional superfields in a "pure spinor superspace" which involves five θ coordinates covariantly contracted with three pure spinors. The bosonic contribution to these amplitudes agrees with the standard results, and we demonstrate identities which show how the t8 and ε10 tensors naturally emerge from integrals over pure spinor superspace. © SISSA 2006.