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<blockquote data-quote="Halbhh" data-source="post: 77078857" data-attributes="member: 375234"><p>I wondered about whether we could make a firm statement like "amplituhedrons require the existence of supersymmetry where each fermion and boson has a corresponding superparticle", as the description at the wiki is: "When the volume of the amplituhedron is calculated in the <a href="https://en.wikipedia.org/wiki/1/N_expansion" target="_blank">planar limit</a> of <a href="https://en.wikipedia.org/wiki/N_%3D_4_super_Yang%E2%80%93Mills" target="_blank"><em>N</em> = 4 <em>D</em> = 4 supersymmetric Yang–Mills theory</a>, it describes the <a href="https://en.wikipedia.org/wiki/Scattering_amplitude" target="_blank">scattering amplitudes</a> of particles described by this theory.<a href="https://en.wikipedia.org/wiki/Amplituhedron#cite_note-Arkani-Hamed_Trnka_2014-1" target="_blank">[1]</a> The amplituhedron thus provides a more intuitive geometric model for calculations with highly abstract underlying principles", where the <em>N</em> = 4 <em>D</em> = 4 supersymmetric Yang–Mills "is a simplified <a href="https://en.wikipedia.org/wiki/Toy_theory" target="_blank">toy theory</a> based on <a href="https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory" target="_blank">Yang–Mills theory</a> that does not describe the real world, but is useful because it can act as a proving ground for approaches for attacking problems in more complex theories." -- so, is it going too far to say that it 'requires the existence of supersymmetry where each fermion and boson has a corresponding superparticle" in that for example what if the supersymmetry models turn out to be just some partial parallel to some (not yet found) more complete theory -- in that case we couldn't yet say what is the overall significance of amplituhedrons (for that matter, for me it's still pretty early and I want to read more and think more on it regardless, and that might take another month).</p></blockquote><p></p>
[QUOTE="Halbhh, post: 77078857, member: 375234"] I wondered about whether we could make a firm statement like "amplituhedrons require the existence of supersymmetry where each fermion and boson has a corresponding superparticle", as the description at the wiki is: "When the volume of the amplituhedron is calculated in the [URL='https://en.wikipedia.org/wiki/1/N_expansion']planar limit[/URL] of [URL='https://en.wikipedia.org/wiki/N_%3D_4_super_Yang%E2%80%93Mills'][I]N[/I] = 4 [I]D[/I] = 4 supersymmetric Yang–Mills theory[/URL], it describes the [URL='https://en.wikipedia.org/wiki/Scattering_amplitude']scattering amplitudes[/URL] of particles described by this theory.[URL='https://en.wikipedia.org/wiki/Amplituhedron#cite_note-Arkani-Hamed_Trnka_2014-1'][1][/URL] The amplituhedron thus provides a more intuitive geometric model for calculations with highly abstract underlying principles", where the [I]N[/I] = 4 [I]D[/I] = 4 supersymmetric Yang–Mills "is a simplified [URL='https://en.wikipedia.org/wiki/Toy_theory']toy theory[/URL] based on [URL='https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory']Yang–Mills theory[/URL] that does not describe the real world, but is useful because it can act as a proving ground for approaches for attacking problems in more complex theories." -- so, is it going too far to say that it 'requires the existence of supersymmetry where each fermion and boson has a corresponding superparticle" in that for example what if the supersymmetry models turn out to be just some partial parallel to some (not yet found) more complete theory -- in that case we couldn't yet say what is the overall significance of amplituhedrons (for that matter, for me it's still pretty early and I want to read more and think more on it regardless, and that might take another month). [/QUOTE]
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