Explaining the Pure Spinor Formalism for the Superstring

Abstract

After adding a pair of non-minimal fields and performing a similarity transformation, the BRST operator in the pure spinor formalism is expressed as a conventional-looking BRST operator involving the Virasoro constraint and (b,c) ghosts, together with 12 fermionic constraints. This BRST operator can be obtained by gauge-fixing the Green-Schwarz superstring where the 8 first-class and 8 second-class Green-Schwarz constraints are combined into 12 first-class constraints. Alternatively, the pure spinor BRST operator can be obtained from the RNS formalism by twisting the ten spin-half RNS fermions into five spin-one and five spin-zero fermions, and using the SO(10)/U(5) pure spinor variables to parameterize the different ways of twisting. GSO(-) vertex operators in the pure spinor formalism are constructed using spin fields and picture-changing operators in a manner analogous to Ramond vertex operators in the RNS formalism.

Added two footnotes and references to Baulieu et al

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Cited by in corpus (30)

• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
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• Superstrings on AdS_4 x CP^3 from Supergravity
• Superstrings in AdS
• From Simplified BLG Action to the First-Quantized M-Theory
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• NSR Superstring Measures Revisited
• Ten-Dimensional Super-Twistors and Super-Yang-Mills
• NSR measures on hyperelliptic locus and non-renormalization of 1,2,3-point functions
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• Superstring field theory in the democratic picture
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• Canonical description of D=10 superstring formulated in supertwistor space
• Analytical solutions of pure-spinor superstring field theory
• A Projection to the Pure Spinor Space
• Twistor Origin of the Superstring
• Computations of superstring amplitudes in pure spinor formalism via Cadabra
• Democratic Superstring Field Theory and its Gauge Fixing
• Massless Chiral Supermultiplets of Higher Spins and the $\theta$-Twistor