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The Amplituhedron has recently been popular; it supposedly encodes perturbative scattering amplitudes in a simple, geometric fashion.

What happens to it in a non-perturbative context? Is there still some sort of amplituhedron, somehjow?

If so, a side question:

Can the amplitudihedron be able to solve the problem of 5-Brane scattering amplitudes in M-Theory?

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    $\begingroup$ Regarding the M5-branes... It seems plausible that the worldvolume theory of a stack of M5-branes - which will be some version of (2,0) theory - has an amplituhedron, simply because (2,0) is another conformal, maximal-susy theory. $\endgroup$ – Mitchell Porter Sep 25 '13 at 22:24
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    $\begingroup$ But that's the theory of scattering inside an M5-brane - how the excitations of the M5-brane interact. Scattering of M5-branes from each other, in some more general space-time background, is a different story, and ties into the general problem of how to understand string theory in the most general way possible. $\endgroup$ – Mitchell Porter Sep 25 '13 at 22:27
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    $\begingroup$ The amplituhedron relies heavily on momentum twistors which only work for 4D theories. It may be possible to generalise in some way to higher dimensions but I think that would require a new idea. $\endgroup$ – Philip Gibbs - inactive Sep 26 '13 at 19:30
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    $\begingroup$ You can define twistor space for six space-time dimensions e.g. arxiv.org/abs/1111.2539, and there are many connections between 4d, 5d, and 6d SUSY QFTs, e.g. see Witten's work on Khovanov homology. So point taken, but there's reason to believe it's possible. $\endgroup$ – Mitchell Porter Sep 27 '13 at 0:17
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    $\begingroup$ @MitchellPorter: no expert on this, but one of the lessons learned about the (2,0) theory is that it manifestly has no weak-coupling description. You need to be more precise about "scattering within a M5 brane", otherwise I have a hard time seeing how it's plausible that a "Grassmannian" description exists. $\endgroup$ – Vibert Sep 29 '13 at 12:01

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