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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2601.14407 |
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| _version_ | 1866918298305691648 |
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| author | Craig, Zachary G. |
| author_facet | Craig, Zachary G. |
| contents | We search for a logarithmic 3-form representing the 6-point MHV gravity amplitude, requiring poles only on physical channels and residues matching factorization. Working in the Orlik-Solomon algebra on a De Concini-Procesi wonderful model, we restrict to the S3 x S3 invariant subspace and impose factorization boundary-by-boundary. The intersection of ten compatible 3|3 channels with two compatible 2-particle channels collapses to a unique one-dimensional candidate line. However, enforcing factorization on a crossing channel obstructs any single-valued global representative. We find that an orbit-mixed form, a linear combination over 20 permutation images indexed by bipartitions, satisfies the crossing constraint. This is consistent with a local-system picture: the global gravity form lives in a rank-20 bundle whose monodromy mixes bipartition chambers rather than flipping a single sign. All code and data are provided for reproducibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbital Structure of 6-Point MHV Gravity Forms Craig, Zachary G. High Energy Physics - Theory 81T18, 14F05, 52B40 We search for a logarithmic 3-form representing the 6-point MHV gravity amplitude, requiring poles only on physical channels and residues matching factorization. Working in the Orlik-Solomon algebra on a De Concini-Procesi wonderful model, we restrict to the S3 x S3 invariant subspace and impose factorization boundary-by-boundary. The intersection of ten compatible 3|3 channels with two compatible 2-particle channels collapses to a unique one-dimensional candidate line. However, enforcing factorization on a crossing channel obstructs any single-valued global representative. We find that an orbit-mixed form, a linear combination over 20 permutation images indexed by bipartitions, satisfies the crossing constraint. This is consistent with a local-system picture: the global gravity form lives in a rank-20 bundle whose monodromy mixes bipartition chambers rather than flipping a single sign. All code and data are provided for reproducibility. |
| title | Orbital Structure of 6-Point MHV Gravity Forms |
| topic | High Energy Physics - Theory 81T18, 14F05, 52B40 |
| url | https://arxiv.org/abs/2601.14407 |