Scalar-Scaffolded Gluons and the Combinatorial Origins of Yang-Mills Theory

Abstract

We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order description of Tr ${\varphi }^3$ theory. We propose that in a precise sense the amplitudes for a suitably "stringy" form of these two theories are identical, up to a simple shift of kinematic variables. This connection is made possible by describing the amplitudes for $n$ gluons via a "scalar scaffolding", arising from the scattering of $2n$ colored scalars coming in $n$ distinct pairs of flavors fusing to produce the gluons. Fundamental properties of the "$u$-variables", describing the "binary geometry" for surfaces appearing in the topological expansion, magically guarantee that the kinematically shifted Tr ${\varphi }^3$ amplitudes satisfy the physical properties needed to be interpreted as scaffolded gluons. These include multilinearity, gauge invariance, and factorization on tree- and loop- level gluon cuts. Our "stringy" scaffolded gluon amplitudes coincide with amplitudes in the bosonic string for extra-dimensional gluon polarizations at tree-level, but differ (and are simpler) at loop-level. We provide many checks on our proposal, including matching non-trivial leading singularities through two loops. The simple counting problem underlying the $u$ variables autonomously "knows" about everything needed to convert colored scalar to gluon amplitudes, exposing a striking "discovery" of Yang-Mills amplitudes from elementary combinatorial ideas in kinematic space.

arXiv comment102pages, 38 figures; typo corrected, published version

References in corpus (18)

• New Relations for Gauge-Theory Amplitudes
• Scattering of Massless Particles in Arbitrary Dimension
• The Amplituhedron
• What is the Simplest Quantum Field Theory?
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Positive Geometries and Canonical Forms
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Unwinding the Amplituhedron in Binary
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• New Double Soft Emission Theorems
• Loops and trees
• String amplitudes from field-theory amplitudes and vice versa
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Open String Amplitudes: Singularities, Asymptotics, and New Representations

Cited by in corpus (8)

• Cosmohedra
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• The Geometry of BCFW for ABJM Loop Integrands
• Smooth Splitting and Zeros from On-Shell Recursion
• Higher-Spin and Higher-Point Constraints on Stringy Amplitudes