Scalar-Scaffolded Gluons and the Combinatorial Origins of Yang-Mills Theory
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arXiv
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| Format: | Preprint |
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2023
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| author | Arkani-Hamed, Nima Cao, Qu Dong, Jin Figueiredo, Carolina He, Song |
| author_facet | Arkani-Hamed, Nima Cao, Qu Dong, Jin Figueiredo, Carolina He, Song |
| contents | 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 $ϕ^3$ 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 $ϕ^3$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00041 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scalar-Scaffolded Gluons and the Combinatorial Origins of Yang-Mills Theory Arkani-Hamed, Nima Cao, Qu Dong, Jin Figueiredo, Carolina He, Song High Energy Physics - Theory High Energy Physics - Phenomenology 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 $ϕ^3$ 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 $ϕ^3$ 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. |
| title | Scalar-Scaffolded Gluons and the Combinatorial Origins of Yang-Mills Theory |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2401.00041 |