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<p>The Veneziano amplitude describing the tree-level scattering of four open superstrings is expected to be consistent with unitarity in ten spacetime dimensions. While this follows indirectly from the no-ghost theorem, a direct proof at the level of the amplitude itself only exists for <i>D</i> ≤ 6. In this note, we close this gap by providing a proof for the partial-wave positivity of the Veneziano amplitude in <i>D</i> ≤ 10, derived directly from its representation as the Euler beta function. We also demonstrate that this proof can be modified to show the positivity of a wider family of amplitudes relevant to the <i>S</i>-matrix bootstrap.</p>

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Positivity of the Veneziano amplitude in ten dimensions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月16日

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  • Gareth Mansfield

摘要

The Veneziano amplitude describing the tree-level scattering of four open superstrings is expected to be consistent with unitarity in ten spacetime dimensions. While this follows indirectly from the no-ghost theorem, a direct proof at the level of the amplitude itself only exists for D ≤ 6. In this note, we close this gap by providing a proof for the partial-wave positivity of the Veneziano amplitude in D ≤ 10, derived directly from its representation as the Euler beta function. We also demonstrate that this proof can be modified to show the positivity of a wider family of amplitudes relevant to the S-matrix bootstrap.