We introduce a new positive geometry, the associahedral grid, which provides a geometric realization of the inverse string theory Kawai–Lewellen–Tye kernel. It captures the full ${\alpha }^{\prime }$ dependence of stringified amplitudes for biadjoint scalar ${\varphi }^3$ theory, pions in the nonlinear sigma model (NLSM), and their mixed $\varphi /\pi$ amplitudes, reducing to the corresponding field theory amplitudes in the ${\alpha }^{\prime }\to 0$ 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 $\delta$ shift, recently proposed to relate field theory $\mathrm{Tr}({\varphi }^3)$ and NLSM pion amplitudes, naturally emerges as the leading contribution to the stringy geometry. We show how the connection between $\mathrm{Tr}({\varphi }^3)$ and NLSM can be geometrized using the associahedral grid.

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• Nonlinear sigma model
• Perturbation theory
• Quantum field theory
• Scattering amplitudes
• String dualities
• Strings & branes
• Field & string theory models & techniques
• Geometry