Large deformations of Tr($Φ^3$) and the world at infinity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909596517400576 |
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| author | Paranjape, Shruti Skowronek, Marcos Spradlin, Marcus Volovich, Anastasia |
| author_facet | Paranjape, Shruti Skowronek, Marcos Spradlin, Marcus Volovich, Anastasia |
| contents | The amplitudes of the non-linear sigma model can be obtained from those of Tr($Φ^3$) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr($Φ^3$) 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_11253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large deformations of Tr($Φ^3$) and the world at infinity Paranjape, Shruti Skowronek, Marcos Spradlin, Marcus Volovich, Anastasia High Energy Physics - Theory The amplitudes of the non-linear sigma model can be obtained from those of Tr($Φ^3$) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr($Φ^3$) 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. |
| title | Large deformations of Tr($Φ^3$) and the world at infinity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.11253 |