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<p>The amplitudes of the non-linear sigma model can be obtained from those of Tr(Φ<sup>3</sup>) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr(Φ<sup>3</sup>) amplitudes under a general class of large kinematic shifts called <i>g</i>-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 <i>g</i>-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.</p>

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Large deformations of Tr(Φ3) and the world at infinity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月12日

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  • Shruti Paranjape,
  • Marcos Skowronek,
  • Marcus Spradlin,
  • Anastasia Volovich

摘要

The amplitudes of the non-linear sigma model can be obtained from those of Tr(Φ3) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr(Φ3) 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.