Covariant one-loop amplitudes in image Original Research Article

We generalize to the eleven-dimensional superparticle Berkovitsʹ prescription for loop computations in the pure spinor approach to covariant quantization of the superstring. Using these ten- and eleven-dimensional results, we compute covariantly the following one-loop amplitudes: image in M-theory; image in type II string theory and image in type I. We also verify the consistency of the formalism in eleven dimensions by recovering the correct classical action from tree-level amplitudes. As the superparticle is only a first approximation to the supermembrane, we comment on the possibility of extending this construction to the latter. Finally, we elaborate on the relationship between the present BRST language and the spinorial cohomology approach to corrections of the effective action.