Antipodal Self-Duality for a Four-Particle Form Factor
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arXiv
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| Format: | Preprint |
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2022
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| author | Dixon, Lance J. Gürdoğan, Ömer Liu, Yu-Ting McLeod, Andrew J. Wilhelm, Matthias |
| author_facet | Dixon, Lance J. Gürdoğan, Ömer Liu, Yu-Ting McLeod, Andrew J. Wilhelm, Matthias |
| contents | We bootstrap the symbol of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. When minimally normalized, this symbol involves only 34 letters and obeys the extended Steinmann relations in all partially-overlapping three-particle momentum channels. In addition, the remainder function for this form factor exhibits an antipodal self-duality: it is invariant under the combined operation of the antipodal map defined on multiple polylogarithms -- which reverses the order of the symbol letters -- and a simple kinematic map. This self-duality holds on a four-dimensional parity-preserving kinematic hypersurface. It implies the antipodal duality recently noticed between the three-particle form factor and the six-particle amplitude in this theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_02410 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Antipodal Self-Duality for a Four-Particle Form Factor Dixon, Lance J. Gürdoğan, Ömer Liu, Yu-Ting McLeod, Andrew J. Wilhelm, Matthias High Energy Physics - Theory High Energy Physics - Phenomenology We bootstrap the symbol of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. When minimally normalized, this symbol involves only 34 letters and obeys the extended Steinmann relations in all partially-overlapping three-particle momentum channels. In addition, the remainder function for this form factor exhibits an antipodal self-duality: it is invariant under the combined operation of the antipodal map defined on multiple polylogarithms -- which reverses the order of the symbol letters -- and a simple kinematic map. This self-duality holds on a four-dimensional parity-preserving kinematic hypersurface. It implies the antipodal duality recently noticed between the three-particle form factor and the six-particle amplitude in this theory. |
| title | Antipodal Self-Duality for a Four-Particle Form Factor |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2212.02410 |