Tree-level amplitudes from the pure spinor superstring

Abstract

We give a comprehensive review of recent developments on using the pure spinor formalism to compute massless superstring scattering amplitudes at tree level. The main results of the pure spinor computations are placed into the context of related topics including the color-kinematics duality in field theory and the mathematical structure of ${\alpha }^{\prime }$-corrections.

196 pp. Invited review for Physics Reports. We welcome the readers' help in spotting typos or technical mistakes. Every correction that is firstly brought to our attention will be rewarded with 20 Euro Cent per numbered equation, to be paid in cash during the next in-person encounter with one of the authors. v2: version accepted for publication in Physics Reports

References in corpus (86)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• ICTP Lectures on Covariant Quantization of the Superstring
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• R^4, purified
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Gravity and Yang-Mills Amplitude Relations
• Gravity from Rational Curves
• New Higher-Derivative $R^4$ Theorems
• Multi-Gluon Scattering in Open Superstring Theory
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• 5 loops in 24/5 dimensions
• Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• New Relations for Einstein-Yang-Mills Amplitudes
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Free field world-sheet correlators for ${\mathrm{AdS}}_3$
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Six Gluon Open Superstring Disk Amplitude, Multiple Hypergeometric Series and Euler-Zagier Sums
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Amplitude for N-Gluon Superstring Scattering
• Supersymmetry Relations and MHV Amplitudes in Superstring Theory
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• The One-Loop Five-Graviton Amplitude and the Effective Action
• Expansion of All Multitrace Tree Level EYM Amplitudes
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Explaining the Pure Spinor Formalism for the Superstring
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
• Complete Six-Gluon Disk Amplitude in Superstring Theory
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Generating series of all modular graph forms from iterated Eisenstein integrals
• PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions
• Amplitudes, Hopf algebras and the colour-kinematics duality
• The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism
• Superstring loop amplitudes from the field theory limit
• Monodromy relations from twisted homology
• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
• Scattering Massive String Resonances through Field-Theory Methods
• Loop amplitudes monodromy relations and color-kinematics duality
• Modular Forms and $SL(2,\mathbb{Z})$-covariance of type IIB superstring theory
• Explaining Pure Spinor Superspace
• Kinematic Hopf algebra for amplitudes and form factors
• Higher-loop amplitudes in the non-minimal pure spinor formalism
• Unitarity Cuts of the Worldsheet
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Modular graph forms from equivariant iterated Eisenstein integrals
• BRST quantization of the pure spinor superstring
• Color-kinematics duality from the Bern-Kosower formalism
• The b Ghost of the Pure Spinor Formalism is Nilpotent
• Local BCJ numerators for ten-dimensional SYM at one loop
• Two-loop superstring five-point amplitudes III, construction via the RNS formulation: even spin structures
• Comparing efficient computation methods for massless QCD tree amplitudes: Closed Analytic Formulae versus Berends-Giele Recursion
• Thread-Scalable Evaluation of Multi-Jet Observables
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Planar binary trees in scattering amplitudes
• Superstrings in General Backgrounds
• Fermionic superstring loop amplitudes in the pure spinor formalism
• Two dialects for KZB equations: generating one-loop open-string integrals
• Lectures on modular forms and strings
• On Pure Spinor Superfield Formalism
• Nonperturbative definition of closed string theory via open string field theory
• Relating the $b$ ghost and the vertex operators of the pure spinor superstring
• Open-string integrals with multiple unintegrated punctures at genus one
• The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes
• Closed string disk amplitudes in the pure spinor formalism
• Type I Supergravity Effective Action from Pure Spinor Formalism
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
• Pure spinor formulation of the superstring and its applications
• KK-like relations of ${\alpha }^{\prime }$ corrections to disk amplitudes
• Snowmass White Paper: Bootstrapping String Theory
• On the $\mathcal{N}$ = 4, d = 4 pure spinor measure factor
• General (anti-)commutators of gamma matrices
• The physical states of the Hybrid Formalism
• "GammaMaP" - A Mathematica Package for Clifford Algebras, Gamma Matrices and Spinors
• Computations of superstring amplitudes in pure spinor formalism via Cadabra
• Manifest Spacetime Supersymmetry and the Superstring

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• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Lorentzian contours for tree-level string amplitudes
• Basis decompositions of genus-one string integrals
• Advanced tools for basis decompositions of genus-one string integrals
• Form factors from string amplitudes
• Chaos and moduli space volumes in unorientable JT gravity
• Superstring amplitudes meet surfaceology
• Twisted de Rham theory for string double copy in AdS
• Tension between string amplitude prescriptions with presumed spacetime supersymmetry