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Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

Nathan Berkovits
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Abstract

A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable $b$ ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that $R^4$ terms in the effective action receive no perturbative contributions above one loop.

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Nathan Berkovits. 2004-09-22. Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring. https://doi.org/10.1088/1126-6708%2F2004%2F09%2F047

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