Register

Adv. Query

Q&A (4871)

Reviews (203)

Open problems (47)
Meta (439)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

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

3575 views

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 ]

Your comment on this question:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if my answer is selected or commented on:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverf$\varnothing$ow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).

Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights

...