10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action

Abstract

Using the pure spinor master action for 10D super-Yang-Mills in the gauge b 0 V = QΞ, tree-level scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested b-ghost operators, and show that the Siegel gauge condition b 0 V = 0 gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from the Jacobi identity of a kinematic algebra.

A Minimal b Ghost

“…The algebraic behaviour of b are essential for proving properties of amplitudes like color-kinematics duality and double copy. [21,[30][31][32] Its failure to be a derivation defines the brackets for the kinetic Lie algebra. We have not examined this in detail for b ′ .…”

“…For useful rewritings, see in particular ref. [21]. We use conventions where the torsion is T 𝛼𝛽 a = 2𝛾 a 𝛼𝛽 , i.e., {D 𝛼 , D 𝛽 } = −2𝛾 a 𝛼𝛽 .…”

“…The rewriting of the b operator in terms of physical operators in refs. [20,21] is probably one of the deepest and physically most meaningful ones. We expect it to hold equally in minimal variables.…”

Manifest colour-kinematics duality and double-copy in the string-based formalism

“…In principle it can be applied to any theory as soon as we guarantee multi-particle fields in the BCJ gauge. One first example should be the case where the BCJ gauge originally appeared, ten-dimensional N = 1 super Yang-Mills in [17] (more recently from a new approach in [59]), but for now we will restrict our presentation only to cases without supersymmetry.…”