Fermionic superstring loop amplitudes in the pure spinor formalism

The pure spinor formulation of the ten-dimensional super string leads to manifestly supersymmmetric loop amplitudes, expressed as integrals in pure spinor superspace. This paper explores different methods to evaluate these integrals and then uses them to calculate the kinematic factors of the one-loop and two-loop massless four-point amplitudes involving two and four Ramond states.