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

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

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,851 answers , 20,619 comments
1,470 users with positive rep
501 active unimported users
More ...

What's the Coulomb Branch and why is it important?

+ 5 like - 0 dislike
11 views

I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the Coulomb branch. I have searched the concept but I always find very long and complex explanations. Could anyone explain it in a direct way, pointing out some physical intuition?

This post imported from StackExchange Physics at 2016-07-13 17:22 (UTC), posted by SE-user miguelFe
asked Mar 6, 2014 in Theoretical Physics by miguelFe (50 points) [ no revision ]

1 Answer

+ 1 like - 0 dislike

If the vacuum of the theory is supersymmetric - i.e. SUSY is not broken - then it is annihilated by the SUSY generators. On the other hand, using the SUSY algebra one can show that the hamiltonian can be written in terms of the SUSY generators. This implies that the vacuum $|0\rangle$ is supersymmetric if and only if $\langle 0|H|0\rangle=0$, i.e. the vev of the order parameters of the theory vanishes. The classical moduli space is defined as the space of the scalar field configurations that vanish the scalar potential of the theory.

Now consider $\mathcal N=2$ Super Yang-Mills. This theory has three dynamic scalar fields, one of them is in the adjoint of the gauge group (supermultiplet) and the other two in an arbitrary representation (hypermultiplet). The configurations with non vanishing vev for the scalar in the adjoint and vanishing vev for the hypermultiplet scalars form the Coulomb branch of the moduli space. The configurations with vanishing vev for the scalar in the adjoint and a non vanishing vev for the scalars in other representation than the adjoint form the Higgs branch of the theory.

The main importance of these branches in my opinion is that they characterize different phases of supersymmetric gauge theories. A little bit more can be found here: What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?

This post imported from StackExchange Physics at 2016-07-13 17:22 (UTC), posted by SE-user Diracology
answered May 2, 2016 by Diracology (90 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$\hbar$ysi$\varnothing$sOverflow
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).
To avoid this verification in future, please log in or register.




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

Your rights
...