Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Dual conformal symmetry and spin networks in ABJM

+ 7 like - 0 dislike
938 views

In this question, I would love to hear some independent opinions on an issue I asked Juan Maldacena, Nathan Berkovits, Dan Jafferis, and others, but all the physicists may be missing something. The question has 2 main parts:

  1. Is there a dual superconformal symmetry in 2+1-dimensional ABJM theories? In what limit does it apply? (For $N=4$ gauge theory, it's the planar limit, but what is the counterpart in 2+1 dimensions?)
  2. Are there spin network states in this extension of Chern-Simons theory? Can their expectation values be related to scattering amplitudes in the ABJM theory, much like the piecewise null Wilson loops are related to scattering amplitudes in $N=4$ gauge theory?

Concerning the first question, there's some confusion what $N$ should go to infinity and what should be kept fixed, especially when it comes to the scaling of the level $k$ in the limit. In string theory, the dual superconformal symmetry (and the Yangian) is very constraining - but that's because it still constrains a lot of the "stringy stuff".

Should one necessarily go to the limit with the stringy stuff - e.g. a high-level, a $CP^3$ compactification of type IIA - to see some dual superconformal symmetry? Or is there a dual superconformal symmetry that only works in the planar limit which simply means that only the (leading?) SUGRA amplitudes are constrained?

Concerning the second question, the ABJM theory secretly contains membranes, and their discretization - analogous to the piecewise null Wilson loops - could involve faces (pieces of membranes?) surrounded by open Wilson lines. Are they gauge-invariant?

This post imported from StackExchange Physics at 2014-06-07 05:13 (UCT), posted by SE-user Luboš Motl
asked Feb 20, 2011 in Theoretical Physics by Luboš Motl (10,278 points) [ no revision ]
What is the ABJM theory? ... Ok. I got it. Aharony, Bergman, Jafferis and Maldacena

This post imported from StackExchange Physics at 2014-06-07 05:13 (UCT), posted by SE-user user346
can you point me to sources where I can learn how piecewise null Wilson loops are related to scattering amplitudes in N=4 gauge theory?

This post imported from StackExchange Physics at 2014-06-07 05:13 (UCT), posted by SE-user user346
Yes, ABJM is them: arxiv.org/abs/0806.1218

This post imported from StackExchange Physics at 2014-06-07 05:13 (UCT), posted by SE-user Luboš Motl
The piecewise null Wilson loops to calculate the amplitudes were started by Alday and Maldacena etc. xxx.lanl.gov/abs/0705.0303 but see my popular review of the twistor uprising for other references: motls.blogspot.com/2011/01/twistor-minirevolution-goes-on.html

This post imported from StackExchange Physics at 2014-06-07 05:13 (UCT), posted by SE-user Luboš Motl

1 Answer

+ 4 like - 0 dislike

My wild idea would be to look for holomorphic linking of Wilson loops in the ABJM theory, working from its conjectured Grassmannian integral representation.

This post imported from StackExchange Physics at 2014-06-07 05:13 (UCT), posted by SE-user Mitchell Porter
answered Feb 20, 2011 by Mitchell Porter (1,950 points) [ no revision ]
Very interesting...

This post imported from StackExchange Physics at 2014-06-07 05:13 (UCT), posted by SE-user Luboš Motl

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):
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$\hbar$ysics$\varnothing$verflow
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
...