Register

Adv. Query

Q&A (4870)

Reviews (203)

Open problems (47)
Meta (439)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

How do I reconcile the representation theoretic picture of the central charge in a CFT with the physical picture of the same?

942 views

By a representation theoretic picture I mean viewing the central charge as something that arises as an obstruction to lifting a projective representation of the Witt algebra of the generators of conformal transformations into a linear representation, while by a physical picture I mean viewing it as something to do with the Casimir energy and the trace of the stress tensor.

asked May 27, 2014 in Theoretical Physics by Arpan Saha (50 points) [ revision history ]

One can think about more general anomalies and see the two perspectives there. The first picture has something to do with the symmetry group (in this case the conformal group) failing to commute with certain observables (eg. the L operators). The second picture is when we compute expectation values of these operators (eg. the stress tensor) they transform under the symmetries.

commented May 27, 2014 by Ryan Thorngren (1,925 points) [ no revision ]

Your comment on this question:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

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):

Email me at this address if my answer is selected or commented on:

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$\hbar$ysics$\varnothing$verflow
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

...