Relating the RNS and Pure Spinor Formalisms for the Superstring

Abstract

Recently, the superstring was covariantly quantized using the BRST-like operator $Q=\oint {\lambda }^{\alpha }{d}_{\alpha }$ where ${\lambda }^{\alpha }$ is a pure spinor and $d_{\alpha }$ are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and ${\eta }_0$ ghost. This map is then used to relate physical vertex operators and tree amplitudes in the two formalisms. Furthermore, the map implies the existence of a $b$ ghost in the pure spinor formalism which might be useful for loop amplitude computations.

26 pages harvmac tex

Cited by in corpus (65)

• Pure Spinor Formalism as an N=2 Topological String
• Ten-Dimensional Supergravity Constraints from the Pure Spinor Formalism for the Superstring
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• R^4, purified
• Covariant Quantization of Superstrings Without Pure Spinor Constraints
• Covariant One-Loop Amplitudes in D=11
• Massive Superstring Vertex Operator in D=10 Superspace
• Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring
• The Superembedding Origin of the Berkovits Pure Spinor Covariant Quantization of Superstrings
• Supersymmetric Born-Infeld from the Pure Spinor Formalism of the Open Superstring
• Scattering Equations and String Theory Amplitudes
• Origin of Pure Spinor Superstring
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Towards a Worldsheet Derivation of the Maldacena Conjecture
• A New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring
• Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism
• Tree-level amplitudes from the pure spinor superstring
• Explaining the Pure Spinor Formalism for the Superstring
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• Y-formalism in Pure Spinor Quantization of Superstrings
• Higher genus superstring amplitudes from the geometry of moduli spaces
• Ghost constraints and the covariant quantization of the superparticle in ten dimensions
• On the b-antighost in the Pure Spinor Quantization of Superstrings
• Superstrings in AdS
• Current Algebra of the Pure Spinor Superstring in AdS(5) x S(5)
• Relating Green-Schwarz and Extended Pure Spinor Formalisms by Similarity Transformation
• Operator Mapping between RNS and Extended Pure Spinor Formalisms for Superstring
• Covariant Multiloop Superstring Amplitudes
• BRST quantization of the pure spinor superstring
• Pure-spinor superstrings in d=2,4,6
• The b Ghost of the Pure Spinor Formalism is Nilpotent
• From the Geometry of Pure Spinors with their Division Algebras to Fermion's Physics
• Correlation Functions in Berkovits' Pure Spinor Formulation
• The Massless Spectrum of Covariant Superstrings
• D-Brane Boundary States in the Pure Spinor Superstring
• Democratic Superstring Field Theory: Gauge Fixing
• Pure Spinor Strings in TsT Deformed Background
• Amplitudes Involving Massive States Using Pure Spinor Formalism
• Worldline Approach of Topological BF Theory
• BRST Anomaly and Superspace Constraints of the Pure Spinor Heterotic String in a Curved Background
• Theta Expansion of First Massive Vertex Operator in Pure Spinor
• Non-Critical Pure Spinor Superstrings
• Note About Classical Dynamics of Pure Spinor String on AdS_5 x S_5 Background
• Integrated Massive Vertex Operator in Pure Spinor Formalism
• Decoupling of unphysical states in the minimal pure spinor formalism I
• Spectrum generating algebra for the pure spinor superstring
• Covariant Map Between Ramond-Neveu-Schwarz and Pure Spinor Formalisms for the Superstring
• On D-Brane Boundary State Analysis in Pure-Spinor Formalism
• B-RNS-GSS heterotic string in curved backgrounds
• The Pure Spinor Formulation of Superstrings
• Three-Graviton Amplitude in Berkovits-Vafa-Witten Variables
• Towards the underlying gauge theory of the pure spinor superstring
• Relating the $b$ ghost and the vertex operators of the pure spinor superstring
• On the field-antifield (a)symmetry of the pure spinor superstring
• Note About Redefinition of BRST Operator for Pure Spinor String in General Background
• Spin fields for the spinning particle
• Non-BPS D-Branes in Light-Cone Green-Schwarz Formalism
• Canonical description of D=10 superstring formulated in supertwistor space
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• New Superembeddings for Type II Superstrings
• Analytical solutions of pure-spinor superstring field theory
• Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --
• Massless Chiral Supermultiplets of Higher Spins and the $\theta$-Twistor
• Manifest Spacetime Supersymmetry and the Superstring
• On Democratic String Field Theories