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 ...

  Relevance of operators in 4d N=1 theories

+ 4 like - 0 dislike
581 views

I have a conceptual question about how to judge a given operator, \(\mathcal{O}\), in 4d \(\mathcal{N}=1\) theories is relevant or not.

In the literature, the criterion is given by \(R(\mathcal{O}) \leqslant 2\).  i.e., the operator is relevant or marginal if \(R(\mathcal{O}) \leqslant 2\). However, as I understand, an acceptable operator deformation for the theory must have \(R(\mathcal{O}) = 2\) so that \(R\)-symmetry is not broken.

How to understand why the \(R\)-charge, not the dimension of the operator, tells us that the operator is relevant, marginal or irrelevant? Are there any relations when the theory is in UV? How to resolve the "contradiction" that the \(R\)-charge for the superpotential should always be such that \(R=2\)?

asked Apr 1, 2015 in Theoretical Physics by Ke Ye (50 points) [ revision history ]
retagged Apr 19, 2015 by dimension10

1 Answer

+ 3 like - 0 dislike

For a general quantum field theory, it's true that the notions of relevant, marginal, irrelevant operators are defined in terms of dimensions of operators. In the special case of a supersymmetric theory, it is natural to study the special case of supersymmetric deformations and the familiar criterion in terms of dimensions can often be reformulated.

More precisely, in a unitary 4d N=1 superconformal field theory, there is a general ("BPS-like") bound, bounding below the dimension of an operator by a multiple of its R-charge. Operators inducing supersymmetric deformations are precisely the operators saturating this bound (chiral or antichiral). For such operators, dimension and R-charge determine each other and so the definition of relevant, marginal, irrelevant can be reformulated purely in tems of R-charge.

The condition R=2 is equivalent to the condition of marginality, itself equivalent to the preservation of R-symmetry. Indeed, R-symmetry is only guaranteed to be preserved in the superconformal case. In the non-superconformal case, R-symmetry is in general anomalous.  

answered Aug 14, 2018 by 40227 (5,140 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$\hbar$ysicsOverfl$\varnothing$w
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
...