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<p>We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work [1] showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the fusion category data. By imposing unitarity, symmetry and the modified crossing, we constrain the space of consistent S-matrices, identifying integrable theories with non-invertible symmetries at the cusps of allowed regions. We also extend the modified crossing rules to cases where vacua transform in non-regular representations of fusion category, utilizing a connection to a dual category <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25860_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi mathvariant="script">C</mi> <mi mathvariant="script">M</mi> <mo>∗</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{C}}_{\mathcal{M}}^{\ast } \)</EquationSource> </InlineEquation> and Symmetry Topological Field Theory (SymTFT). This highlights the utility of SymTFT in the analysis of scattering amplitudes.</p>

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S-matrix bootstrap and non-invertible symmetries

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月28日

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  • Christian Copetti,
  • Lucía Córdova,
  • Shota Komatsu

摘要

We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work [1] showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the fusion category data. By imposing unitarity, symmetry and the modified crossing, we constrain the space of consistent S-matrices, identifying integrable theories with non-invertible symmetries at the cusps of allowed regions. We also extend the modified crossing rules to cases where vacua transform in non-regular representations of fusion category, utilizing a connection to a dual category C M ∗ \( {\mathcal{C}}_{\mathcal{M}}^{\ast } \) and Symmetry Topological Field Theory (SymTFT). This highlights the utility of SymTFT in the analysis of scattering amplitudes.