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# Pure spinor formulation of the superstring and its applications

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## 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.

Text
2210.10510v1 - Author's Original

Accepted/In Press date: 19 October 2022
e-pub ahead of print date: 19 October 2022
Additional Information: 42 pp, Overview written for the "Handbook of Quantum Gravity", eds. C. Bambi, L. Modesto and I. Shapiro
Keywords: hep-th

## Identifiers

Local EPrints ID: 472045
URI: http://eprints.soton.ac.uk/id/eprint/472045
PURE UUID: 9fc43390-be35-4c70-82e6-18f3f9a10b5d
ORCID for Carlos R. Mafra: orcid.org/0000-0001-9842-9654

## Catalogue record

Date deposited: 24 Nov 2022 17:38

## Contributors

Author: Nathan Berkovits
Author: Carlos R. Mafra