Covariant One-Loop Amplitudes in D=11

TL;DR

This paper extends the pure spinor formalism to eleven dimensions, enabling covariant computation of one-loop amplitudes in M-theory and string theories, and verifies the formalism's consistency with known classical actions.

Contribution

It generalizes Berkovits' prescription to eleven dimensions and computes key one-loop amplitudes, bridging superparticle and supermembrane formalisms.

Findings

Computed covariant one-loop amplitudes in M-theory and string theories.

Verified the formalism reproduces known classical actions.

Discussed potential extension to supermembranes.

Abstract

We generalize to the eleven-dimensional superparticle Berkovits' 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: C\wedge X_8 in M-theory; B\wedge X_8 in type II string theory and F^4 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.