Pure spinor formulation of the superstring and its applications

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 $Ad{S}_5\times S^5$ 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.

42 pp, Overview written for the "Handbook of Quantum Gravity", eds. C. Bambi, L. Modesto and I. Shapiro. v2: references and acknowledgements added, typos removed

References in corpus (13)

• New Relations for Gauge-Theory Amplitudes
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism
• Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Superstring loop amplitudes from the field theory limit
• The b Ghost of the Pure Spinor Formalism is Nilpotent
• Local BCJ numerators for ten-dimensional SYM at one loop
• $Ad{S}_5\times S^5$ supergravity vertex operators
• Manifest Spacetime Supersymmetry and the Superstring

Cited by in corpus (1)

• Tree-level amplitudes from the pure spinor superstring