Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism

Abstract

We use the non-minimal pure spinor formalism to compute in a super-Poincare covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these amplitudes are expressed as integrals of ten-dimensional superfields in a "pure spinor superspace" which involves five $\theta$ coordinates covariantly contracted with three pure spinors. The bosonic contribution to these amplitudes agrees with the standard results, and we demonstrate identities which show how the $t_8$ and ${\epsilon }_{10}$ tensors naturally emerge from integrals over pure spinor superspace.

20 pages, harvmac tex

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Cited by in corpus (60)

• Explicit BCJ Numerators from Pure Spinors
• The closed-string 3-loop amplitude and S-duality
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• Berends-Giele recursions and the BCJ duality in superspace and components
• String-inspired BCJ numerators for one-loop MHV amplitudes
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• String predictions for near future colliders from one-loop scattering amplitudes around D-brane worlds
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Simplifying the Tree-level Superstring Massless Five-point Amplitude
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• Pure spinor superfields -- an overview
• Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
• Tree-level amplitudes from the pure spinor superstring
• Double-Copy Structure of One-Loop Open-String Amplitudes
• Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
• Toward the Determination of R^3F^2 Terms in M-theory
• PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics
• Cohomology foundations of one-loop amplitudes in pure spinor superspace
• One-loop Superstring Amplitude From Integrals on Pure Spinors Space
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• The D^{10} R^4 term in type IIB string theory
• Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach
• Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation
• Perfecting one-loop BCJ numerators in SYM and supergravity
• The two-loop superstring five-point amplitude and S-duality
• BRST quantization of the pure spinor superstring
• Local BCJ numerators for ten-dimensional SYM at one loop
• On gauge couplings and thresholds in Type I Gepner models and otherwise
• Supersymmetry Breaking Effects using the Pure Spinor Formalism of the Superstring
• First-quantized N=4 Yang-Mills
• Amplitudes Involving Massive States Using Pure Spinor Formalism
• Fermionic superstring loop amplitudes in the pure spinor formalism
• Theta Expansion of First Massive Vertex Operator in Pure Spinor
• Integrated Massive Vertex Operator in Pure Spinor Formalism
• Decoupling of unphysical states in the minimal pure spinor formalism I
• One-loop superstring six-point amplitudes and anomalies in pure spinor superspace
• On Pure Spinor Superfield Formalism
• Decoupling of unphysical states in the minimal pure spinor formalism II
• Type I Supergravity Effective Action from Pure Spinor Formalism
• Scattering of massive open strings in pure spinor
• Scattering equations, supergravity integrands, and pure spinors
• Two-Point Superstring Tree Amplitudes Using the Pure Spinor Formalism
• Taming the 11D pure spinor b-ghost
• Geometric counter-vertex for open string scattering on D-branes
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• Pure spinor formulation of the superstring and its applications
• Pure spinor computation towards open string three-loop
• RNS and Pure Spinors Equivalence for Type I Tree Level Amplitudes Involving up to Four Fermions
• A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism
• Superstring Sigma Model Computations Using the Pure Spinor Formalism