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arXiv · 2504.11253

Large deformations of Tr($\Phi^3$) and the world at infinity

Shruti Paranjape·Marcos Skowronek·Marcus Spradlin·Anastasia Volovich
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Abstract

The amplitudes of the non-linear sigma model can be obtained from those of Tr($\Phi^3$) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr($\Phi^3$) amplitudes under a general class of large kinematic shifts called $g$-vector shifts. The objects that live in this world at infinity retain certain key amplitude-like properties, most notably factorization, and admit descriptions in terms of polytopes, but they are not generally amplitudes of any cognizable theory. We identify particular $g$-vector shifts that lead at infinity to mixed amplitudes involving two pions and any number of scalars, allowing us to provide polytopal descriptions of these amplitudes.

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Shruti Paranjape, Marcos Skowronek, Marcus Spradlin, Anastasia Volovich. 2025-04-15. Large deformations of Tr($\Phi^3$) and the world at infinity. https://arxiv.org/abs/2504.11253

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