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<p>The amplituhedron <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="222_2025_1316_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">A</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mn>4</mn> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{A}_{n,k,4}$</EquationSource> </InlineEquation> is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="222_2025_1316_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">A</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mn>4</mn> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{A}_{n,k,4}$</EquationSource> </InlineEquation> admits a decomposition into images of BCFW positroid cells, arising from the Britto–Cachazo–Feng–Witten recurrence (2005). We prove that this conjecture is true.</p>

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The amplituhedron BCFW triangulation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月4日

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  • Chaim Even-Zohar,
  • Tsviqa Lakrec,
  • Ran J. Tessler

摘要

The amplituhedron A n , k , 4 $\mathcal{A}_{n,k,4}$ is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that A n , k , 4 $\mathcal{A}_{n,k,4}$ admits a decomposition into images of BCFW positroid cells, arising from the Britto–Cachazo–Feng–Witten recurrence (2005). We prove that this conjecture is true.