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What happens to the amplituhedron in a non-peturbative context? + Solving 5-brane scattering in M-theory with the amplituhedron?

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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, somehow?

If the answer is "yes", can the amplitudihedron be able to solve the problem of 5-Brane scattering amplitudes in M-Theory?

asked Sep 25, 2013 in Theoretical Physics by dimension10 (1,985 points) [ revision history ]
edited May 8, 2015 by dimension10

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.

This post imported from StackExchange Physics at 2014-03-07 16:34 (UCT), posted by SE-user Mitchell Porter

commented Sep 25, 2013 by Mitchell Porter (1,950 points) [ no revision ]

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.

This post imported from StackExchange Physics at 2014-03-07 16:34 (UCT), posted by SE-user Mitchell Porter

commented Sep 25, 2013 by Mitchell Porter (1,950 points) [ no revision ]

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.

This post imported from StackExchange Physics at 2014-03-07 16:34 (UCT), posted by SE-user Philip Gibbs

commented Sep 26, 2013 by Philip Gibbs (650 points) [ no revision ]

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.

This post imported from StackExchange Physics at 2014-03-07 16:34 (UCT), posted by SE-user Mitchell Porter

commented Sep 26, 2013 by Mitchell Porter (1,950 points) [ no revision ]

@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.

This post imported from StackExchange Physics at 2014-03-07 16:34 (UCT), posted by SE-user Vibert

commented Sep 29, 2013 by Vibert (0 points) [ no revision ]

@Vibert Perhaps it would be the scattering of the tensionless strings? But both N=4 SYM, and ABJM, have Grassmannian descriptions, so it makes sense that (2,0) would, too.

This post imported from StackExchange Physics at 2014-03-07 16:34 (UCT), posted by SE-user Mitchell Porter

commented Sep 29, 2013 by Mitchell Porter (1,950 points) [ no revision ]

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