• 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
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Zumino's consistent and covariant anomalies - applied to quantum hall?

+ 5 like - 0 dislike

What is the `physical' meaning of consistent anomalies and covariant anomalies?

Perhaps a good Reference is: Consistent and covariant anomalies in gauge and gravitational theories - William A. Bardeen and Bruno Zumino

I kind of remember (and used to think) that: $$ \text{consistent anomaly} =(1/2) (\text{covariant anomaly}) $$

So the physical picture I have is, for example a 1+1D system. See a Reference doi.org/10.1103/PhysRevB.107.014311. Consider this 1+1D theory lives as the edge theory on the boundary of a 2+1D spatial cylinder. There is an (integer) quantum hall state with charge U(1) symmetry.

On the left edge, there is a left-moving current with a `consistent' anomaly $$ \partial_\mu J_L^\mu =(e/4\pi)\epsilon^{\mu\nu} F_{\mu\nu}(=\text{consistent anomaly}?) $$

On the right edge, there is a right-moving current with another `consistent' anomaly $$ \partial_\mu J_R^\mu =-(e/4\pi)\epsilon^{\mu\nu} F_{\mu\nu}(=-\text{consistent anomaly}?) $$

Consider putting these two edges more-or-less together as the same 1+1D (but without direct interactions), shows axial anomaly: $$ \partial_\mu J_A^\mu=\partial_\mu (J_L^\mu-J_R^\mu) =(e/2\pi)\epsilon^{\mu\nu} F_{\mu\nu}(=\text{covariant anomaly}?) $$

while vector current conserved: $$ \partial_\mu J_V^\mu=\partial_\mu (J_L^\mu+J_R^\mu) =0 $$

At least, this physical picture produces: $$ \text{consistent anomaly} =(1/2) (\text{covariant anomaly}) $$

Can someone inform whether this is a right picture or not for the consistent anomalies and covariant anomalies?

This post imported from StackExchange Physics at 2014-06-04 11:40 (UCT), posted by SE-user Idear

asked Nov 13, 2013 in Theoretical Physics by wonderich (1,500 points) [ revision history ]
edited Feb 6, 2023 by wonderich
You will find interesting informations page $3$ of the paper you first cited in free access here

This post imported from StackExchange Physics at 2014-06-04 11:40 (UCT), posted by SE-user Trimok

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