Positive Geometry for Stringy Scalar Amplitudes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917181940301824 |
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| author | Bartsch, Christoph Kampf, Karol Podivin, David Stalknecht, Jonah |
| author_facet | Bartsch, Christoph Kampf, Karol Podivin, David Stalknecht, Jonah |
| contents | We introduce a new positive geometry, the associahedral grid, which provides a geometric realization of the inverse string theory KLT kernel. It captures the full $α'$-dependence of stringified amplitudes for bi-adjoint scalar $ϕ^3$ theory, pions in the NLSM, and their mixed $ϕ$/$π$ amplitudes, reducing to the corresponding field theory amplitudes in the $α'\to 0$ limit. Our results demonstrate how positive geometries can be utilized beyond rational functions to capture stringy features of amplitudes, such as an infinite resonance structure. The kinematic $δ$-shift, recently proposed to relate field theory $\mathrm{Tr}(ϕ^3)$ and NLSM pion amplitudes, naturally emerges as the leading contribution to the stringy geometry. We show how the connection between $\mathrm{Tr}(ϕ^3)$ and NLSM can be geometrized using the associahedral grid. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_20161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive Geometry for Stringy Scalar Amplitudes Bartsch, Christoph Kampf, Karol Podivin, David Stalknecht, Jonah High Energy Physics - Theory We introduce a new positive geometry, the associahedral grid, which provides a geometric realization of the inverse string theory KLT kernel. It captures the full $α'$-dependence of stringified amplitudes for bi-adjoint scalar $ϕ^3$ theory, pions in the NLSM, and their mixed $ϕ$/$π$ amplitudes, reducing to the corresponding field theory amplitudes in the $α'\to 0$ limit. Our results demonstrate how positive geometries can be utilized beyond rational functions to capture stringy features of amplitudes, such as an infinite resonance structure. The kinematic $δ$-shift, recently proposed to relate field theory $\mathrm{Tr}(ϕ^3)$ and NLSM pion amplitudes, naturally emerges as the leading contribution to the stringy geometry. We show how the connection between $\mathrm{Tr}(ϕ^3)$ and NLSM can be geometrized using the associahedral grid. |
| title | Positive Geometry for Stringy Scalar Amplitudes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.20161 |