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 b0V = 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 b0V = 0 gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from the Jacobi identity of a kinematic algebra.

Snowmass White Paper: the Double Copy and its Applications

“…23 Also for the NLSM, string-theory methods led to compact all-multiplicity expressions for color-kinematics dual tree-level numerators [44,438]. More general string-motivated perspectives on kinematic Jacobi identities can be obtained from vertex operator algebra constructions [439,440], the pure-spinor master action of ten-dimensional sYM [441] or residue theorems for moduli spaces of Riemann surfaces with marked points [442].…”

“…(1.2), could be expressed as: "understanding gravity is no more complicated than understanding gauge theory." A corollary, emerging from attempts to understand the duality between color and kinematics at the level of equations of motion [140-142, 144, 145, 192, 543-545] and the action [45,428,441], could be phrased "gauge theory need not be more complicated than a scalar theory." To fully realize the idea, it is necessary to write the non-trivial kinematic details of gauge theory as a Lie-algebraic structure that is dual to the color Lie algebra.…”

Snowmass White Paper: String Perturbation Theory

“…Suitable representations of open-string amplitudes lead to solutions of kinematic Jacobi identities at tree-level [84], one loop [85,86] and two loops [46] through their respective point-particle limits [87]. A more general viewpoint on kinematic Jacobi identities is offered by a residue theorem for moduli spaces of Riemann surfaces with marked points [88] and from nested b-ghost action on vertex operators of the pure-spinor formalism in Siegel gauge [89].…”

Off-Shell Color-Kinematics Duality for Chern-Simons

“…µνρ ∂ ρ c. Furthermore, Lorenz gauge implies that the a field is constant, and we set it to zero a = 0.3 The superfield formulation of Chern-Simons theory is reminiscent of the more recent formulation of 10D super-Yang-Mills in terms of a pure-spinor superparticle[205] 4. The notation is inspired by the pure-spinor Feynman rules used in ref [206],. where the corresponding operator is the composite worldline b ghost.…”

“…An alternative is to introduce creation and annihilation operators for the fields carrying loop momenta, but this goes beyond our needs for performing simple field contractions 6. See related considerations for Yang-Mills theory in refs [171,206]…”