• 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.


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


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,064 questions , 2,215 unanswered
5,347 answers , 22,734 comments
1,470 users with positive rep
818 active unimported users
More ...

  Is it possible to couple an odd number of Dirac fermions, at finite density, to a massless gauge field in 2+1d?

+ 2 like - 0 dislike

In a beautiful paper by A. N. Redlich on the parity anomaly (PRL 52, 18 (1984), no arXiv version), the author indicates that an odd number of Dirac fermions can never be coupled to a massless gauge field in 2+1d due to the necessity of introducing background Chern-Simons terms to maintain gauge invariance

"The induced topological term $±W[A]$ in $I_{eff}[A]$ is known to produce a mass for the gauge fields. Not only must parity conservation be violated in odd-dimensional theories with an odd number of fermions, but the gauge fields $\textit{must}$ become massive as well",

where $W[A]$ is the Chern-Simons term and $I_{eff}[A]$ the effective action obtained by integrating out the fermion degrees of freedom.

My question is whether this is still true if the fermions are at a finite density, i.e. one adds a chemical potential such that there is a whole Fermi surface of excitations (in this case, it's my understanding that one cannot simply integrate out the fermions to get $I_{eff}[A]$). Is it possible to couple an odd number of Dirac fermions, at finite density, to a massless gauge field in 2+1d?

Note: I'm glossing over issues to do with whether the presence of massless fermions can stabilise 2+1d gauge theories against confinement (I'm assuming here that they can). Also I don't mind whether parity conservation is preserved or not, it's just the mass of the gauge field I'm interested in.    

asked Aug 19, 2018 in Theoretical Physics by anonymous [ 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:
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