Pure spinor formulation of the superstring and its applications

TL;DR

The paper reviews the pure spinor formalism for superstring theory, highlighting its advantages in manifest supersymmetry, amplitude computations, and applications to backgrounds like AdS5×S5, offering a covariant quantization approach.

Contribution

It provides a comprehensive overview of the pure spinor formalism, including explicit amplitude calculations and applications to complex backgrounds, advancing superstring quantization methods.

Findings

Explicit computation of disk amplitudes with multiple states

Genus one and two amplitude calculations with several external states

Application to covariant quantization in AdS5×S5 background

Abstract

The pure spinor formalism for the superstring has the advantage over the more conventional Ramond-Neveu-Schwarz formalism of being manifestly spacetime supersymmetric, which simplifies the computation of multiparticle and multiloop amplitudes and allows the description of Ramond-Ramond backgrounds. In addition to the worldsheet variables of the Green-Schwarz-Siegel action, the pure spinor formalism includes bosonic ghost variables which are constrained spacetime spinors and are needed for covariant quantization using a nilpotent BRST operator. In this review, several applications of the formalism are described including the explicit computation in D=10 superspace of the general disk amplitude with an arbitrary number of external massless states, genus one amplitudes with up to seven external states, genus two amplitudes with up to five external states, and the low-energy limit of the genus three amplitude with up to four external states. The pure spinor formalism has also been used to covariantly quantize the superstring in an $AdS_5\times S^5$ background and might be useful for proving the AdS-CFT correspondence in the limit of small AdS radius. This is an overview written for the "Handbook of Quantum Gravity", eds. C. Bambi, L. Modesto and I. Shapiro.