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arXiv · 2508.20161

Positive Geometry for Stringy Scalar Amplitudes

Christoph Bartsch·Karol Kampf·David Podivin·Jonah Stalknecht
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Abstract

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.

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Christoph Bartsch, Karol Kampf, David Podivin, Jonah Stalknecht. 2026-01-04. Positive Geometry for Stringy Scalar Amplitudes. https://doi.org/10.1103/lb5l-twsb

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