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<p>We calculate <i>n</i>-point hard string scattering amplitudes (<i>HSSA</i>) with <i>n</i> − 2 tachyons and 2 tensor states at arbitrary mass levels. We discover the stringy scaling behavior of these <i>HSSA</i>. It is found that for <i>HSSA</i> with more than 2 transverse directions, the degree of stringy scaling dim<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25763_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{M}\)</EquationSource> </InlineEquation><sub>2</sub> decreases comparing to the degree of stringy scaling dim<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25763_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{M}\)</EquationSource> </InlineEquation><sub>1</sub> of the <i>n</i> − 1 tachyons and 1 tensor <i>HSSA</i> calculated previously. Moreover, we propose a set of <i>K</i>-identities which is the key to demonstrate the stringy scaling behavior of <i>HSSA</i>. We explicitly prove both the diagonal and off-diagonal <i>K</i>-identities for the 4-point <i>HSSA</i> and give numerical proofs of these <i>K</i>-identities for some higher point <i>HSSA</i>.</p>

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Stringy scaling of multi-tensor hard string scattering amplitudes and the K-identities

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月14日

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  • Sheng-Hong Lai,
  • Jen-Chi Lee,
  • Yi Yang

摘要

We calculate n-point hard string scattering amplitudes (HSSA) with n − 2 tachyons and 2 tensor states at arbitrary mass levels. We discover the stringy scaling behavior of these HSSA. It is found that for HSSA with more than 2 transverse directions, the degree of stringy scaling dim \(\mathcal{M}\) 2 decreases comparing to the degree of stringy scaling dim \(\mathcal{M}\) 1 of the n − 1 tachyons and 1 tensor HSSA calculated previously. Moreover, we propose a set of K-identities which is the key to demonstrate the stringy scaling behavior of HSSA. We explicitly prove both the diagonal and off-diagonal K-identities for the 4-point HSSA and give numerical proofs of these K-identities for some higher point HSSA.