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

143 submissions , 120 unreviewed
3,899 questions , 1,377 unanswered
4,837 answers , 20,502 comments
1,470 users with positive rep
495 active unimported users
More ...

  Non-hermitian connections in Super-Yang Mills

+ 3 like - 0 dislike
102 views

If you have a lagrangian for chiral superfields in 4 dimensions which is also invariant under SU(N) and you try to gauge the symmetry , You introduce a connection $\Gamma$ so as to make $\Phi^{\dagger}\Gamma \Phi$ gauge invariant under super gauge transformation. If $\Gamma$ is hermitian , you have introduced  vector superfields into the lagrangian coupled with the chiral superfields. Now why don't we consider cases in which $\Gamma$ is not hermitian ?

asked Aug 7 in Theoretical Physics by anonymous [ revision history ]

Hopefully this comment isn't nonsense and/or unrelated.  There is a theory called $\mathcal{N}=1^{*}$ which is a massive deformation of $\mathcal{N}=4$ SYM in four-dimensions where you give a mass $M$ to the three chiral superfields $\Phi_{i}$ with $i=1,2,3$.  And indeed, you consider terms in the Lagrangian like $M \Phi^{\dagger} \Phi$.  You really want $M \in \mathbb{C}$ in general as opposed to $M \in \mathbb{R}$.  And in some contexts, this inspires one to consider not merely Hermitian matrix models, but actually holomorphic matrix models.  So I think you probably would want to consider more general $\Gamma$ in your case.  Sorry this isn't too concrete; just a thought.    

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$\hbar$ys$\varnothing$csOverflow
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
...