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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2508.03813 |
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| _version_ | 1866913976953077760 |
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| author | He, Song Shi, Canxin Tang, Yichao Zhang, Yao-Qi |
| author_facet | He, Song Shi, Canxin Tang, Yichao Zhang, Yao-Qi |
| contents | We define the square amplitudes in planar Aharony-Bergman-Jafferis-Maldacena theory (ABJM), analogous to that in $\mathcal{N}{=}4$ super-Yang-Mills theory (SYM). Surprisingly, the $n$-point $L$-loop integrands with fixed $N{:=}n{+}L$ are unified in a single generating function. Similar to the SYM four-point half-BPS correlator integrand, the generating function enjoys a hidden $S_N$ permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar $f$-graphs. Remarkably, through Gram identities it can also be represented as a linear combination of bipartite $f$-graphs which manifest the important property that no odd-multiplicity amplitude exists in the theory. The generating function and these properties are explicitly checked against squared amplitudes for all $n$ with $N{=}4,6,8$. By drawing analogies with SYM, we conjecture some graphical rules the generating function satisfy, and exploit them to bootstrap a unique $N{=}10$ result, which provides new results for $n{=}10$ squared tree amplitudes, as well as integrands for $(n,L){=}(4,6),(6,4)$. Our results strongly suggest the existence of a "bipartite correlator" in ABJM theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hidden Permutation Symmetry of Squared Amplitudes in ABJM Theory He, Song Shi, Canxin Tang, Yichao Zhang, Yao-Qi High Energy Physics - Theory We define the square amplitudes in planar Aharony-Bergman-Jafferis-Maldacena theory (ABJM), analogous to that in $\mathcal{N}{=}4$ super-Yang-Mills theory (SYM). Surprisingly, the $n$-point $L$-loop integrands with fixed $N{:=}n{+}L$ are unified in a single generating function. Similar to the SYM four-point half-BPS correlator integrand, the generating function enjoys a hidden $S_N$ permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar $f$-graphs. Remarkably, through Gram identities it can also be represented as a linear combination of bipartite $f$-graphs which manifest the important property that no odd-multiplicity amplitude exists in the theory. The generating function and these properties are explicitly checked against squared amplitudes for all $n$ with $N{=}4,6,8$. By drawing analogies with SYM, we conjecture some graphical rules the generating function satisfy, and exploit them to bootstrap a unique $N{=}10$ result, which provides new results for $n{=}10$ squared tree amplitudes, as well as integrands for $(n,L){=}(4,6),(6,4)$. Our results strongly suggest the existence of a "bipartite correlator" in ABJM theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules. |
| title | A Hidden Permutation Symmetry of Squared Amplitudes in ABJM Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.03813 |