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.

arXiv comment196 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

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• Notes on the pure spinor b ghost
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• Pure spinor formulation of the superstring and its applications
• General (anti-)commutators of gamma matrices
• On the $\mathcal{N}$ = 4, d = 4 pure spinor measure factor
• RNS and Pure Spinors Equivalence for Type I Tree Level Amplitudes Involving up to Four Fermions
• The physical states of the Hybrid Formalism
• "GammaMaP" - A Mathematica Package for Clifford Algebras, Gamma Matrices and Spinors
• A noncommutative cycle index and new bases of quasi-symmetric functions and noncommutative symmetric functions
• Computations of superstring amplitudes in pure spinor formalism via Cadabra
• Manifest Spacetime Supersymmetry and the Superstring

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• Basis decompositions of genus-one string integrals
• Advanced tools for basis decompositions of genus-one string integrals
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• Chaos and moduli space volumes in unorientable JT gravity
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