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
5,082 questions , 2,232 unanswered
5,353 answers , 22,786 comments
1,470 users with positive rep
820 active unimported users
More ...

  How can we get the Seiberg-Witten curve from M-theory?

+ 4 like - 0 dislike
1695 views

Have people developed a systematic way to get the Seiberg-Witten curve from some M-theoretical (thus non-perturbative) configuration? If so what exactly is this mechanism and does it yield the same results as the "standard" way?

asked Apr 7, 2015 in Theoretical Physics by Outlander (95 points) [ no revision ]
retagged Apr 16, 2015 by dimension10

2 Answers

+ 6 like - 0 dislike

The fundamental initial paper on the study of N=2 four dimensional gauge theories from the M-theory point of view was written by Witten:

http://arxiv.org/abs/hep-th/9703166

The 4d theory is essentially realized on the worldvolume of a stack of M5 branes compactified on the Seiberg-Witten curve. In particular, in this picture, the Seiberg-Witten curve has a clear geometric interpretation. This M-theory description emerges naturally as the strong coupling limit of a maybe more familiar construction in terms of NS5 and D4-branes in type IIA superstring.

As far as I know, it gives the same result as the "standard" way when it is possible to compare both results. One has probably to be careful about the word "systematic". Witten's paper and its many follow-ups have certainly treated large classes of theories but probably not "all" theories can be obtained in this way. The problem of classification of $N=2$ four dimensional gauge theories, the one for which we expect the existence of a Seiberg-Witten curve, is a rather active area of current research. 

answered Apr 7, 2015 by 40227 (5,140 points) [ revision history ]
edited Apr 8, 2015 by 40227
+ 5 like - 0 dislike

Indeed as said above we do get the Seiberg-Witten curve from M-theory. To do this we need to consider the following brane setup in type IIA strings:

Consider $x_0, \ldots, x_{10}$ and put $M$ $NS5$-branes in $x_0, \ldots, x_5$ and $N$ $D4$-branes in $x_0, x_1, x_2, x_3, x_6 $ (and $x_{10}$ in the M-theory setup this updates to an $M5$-brane)  where the $N$ $D4$-branes are suspended between the $M$ $NS$5- branes. Then introduce $2N$ flavor branes attached to those $NS5$-branes sitting in the outermost of the configuration and extended to infinity.The resulting theory is a $d=4$ $\mathcal{N}=2$ $SU(N)^{M-1}$ gauge theory (which asymptotically is conformal). $U(1)_R$ symmetry is realized by a rotation between the $x_4$ and $x_5$ while the $SU(2)_R$ one is realized by the rotation of the $x_7,x_8$ and $x_9$. The configuration I described above is a string/gauge theory interpretation. Now if we take the tension of the branes into account, the configuration has to be modified to include the quantum effects. We can uplift this configuration to M-theory (introducing a circle $x_{10}$) and minimizing the world volume of the corresponding $M5$-brane (ex-$D4$) under fixed boundary condition will yield the Seiberg-Witten curve. This curve describes a dimension two subsurface inside the space spanned by the coordinates  $x_{4},x_5, x_6,x_{10}$. Now, one is not limited to a $d=4$ theory.

It is possible to compactify in the $x_5$ to obtain a $\mathcal{N}=1$ $d=5$ theory. Once we do the compactification we T-dualize along $x_5$ to obtain a system involving $NS$5-branes and $D5$-branes in Type IIB theory. I will stop here but I think this is the reference [hep-th/9706087] to check alongside (alongside Witten's one for $d=4$ theories).

answered Apr 9, 2015 by conformal_gk (3,625 points) [ no revision ]

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$\hbar$ysicsOver$\varnothing$low
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
...