Computational Tools for Trees in Gauge Theory and Gravity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916076764266496 |
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| author | Bourjaily, Jacob L. |
| author_facet | Bourjaily, Jacob L. |
| contents | We describe a new set of public, self-contained, and versatile computational tools for the investigation, manipulation, and evaluation of tree-level amplitudes in pure (super)Yang-Mills and (super)Gravity, $ϕ^p$-scalar field theory, and various other theories related to these through the double-copy.
The package brings together a diverse set of frameworks for representing amplitudes, from twistor string theory and scattering equations, to KLT and the double-copy, to on-shell recursion and the (oriented) positroid geometry of the amplituhedron. In addition to checking agreement across frameworks, we have made it easy to test many of the non-trivial relations satisfied by amplitudes, their components and building blocks, including: Ward identities, KK and BCJ relations, soft theorems, and the $E_{7|7}$ structure of maximal supergravity.
Beyond providing a coherent and consistent implementation of many well known (if not publicly available) results, our package includes a number of results well beyond what has existed in the present literature--from local, covariant, manifestly color-kinematic-dual representations of amplitudes for gluons/gravitons at arbitrary multiplicity, to a complete classification of Yangian invariants via oriented homology in the amplituhedron.
The Mathematica package `tree_amplitudes', and a notebook illustrating its functionality are available as ancillary files attached to this work's page on the arXiv. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17745 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computational Tools for Trees in Gauge Theory and Gravity Bourjaily, Jacob L. High Energy Physics - Theory We describe a new set of public, self-contained, and versatile computational tools for the investigation, manipulation, and evaluation of tree-level amplitudes in pure (super)Yang-Mills and (super)Gravity, $ϕ^p$-scalar field theory, and various other theories related to these through the double-copy. The package brings together a diverse set of frameworks for representing amplitudes, from twistor string theory and scattering equations, to KLT and the double-copy, to on-shell recursion and the (oriented) positroid geometry of the amplituhedron. In addition to checking agreement across frameworks, we have made it easy to test many of the non-trivial relations satisfied by amplitudes, their components and building blocks, including: Ward identities, KK and BCJ relations, soft theorems, and the $E_{7|7}$ structure of maximal supergravity. Beyond providing a coherent and consistent implementation of many well known (if not publicly available) results, our package includes a number of results well beyond what has existed in the present literature--from local, covariant, manifestly color-kinematic-dual representations of amplitudes for gluons/gravitons at arbitrary multiplicity, to a complete classification of Yangian invariants via oriented homology in the amplituhedron. The Mathematica package `tree_amplitudes', and a notebook illustrating its functionality are available as ancillary files attached to this work's page on the arXiv. |
| title | Computational Tools for Trees in Gauge Theory and Gravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.17745 |