Register

Adv. Query

Q&A (4872)

Reviews (203)

Open problems (47)
Meta (439)

Site Statistics

206 submissions , 164 unreviewed
5,103 questions , 2,249 unanswered
5,355 answers , 22,801 comments
1,470 users with positive rep
820 active unimported users
More ...

Is there a "direct" way to see why the irreversibility of the RG flow is needed for the the enhancement of scale invariance to conformal invariance?

1803 views

In this paper, the author investigates under what conditions scale invariance of a quantum field theory is enhanced to the full conformal symmetry by making use of a holographic argument.

The argument outlined in the introduction contains that the scale invariance of a quantum field theory can only be enhanced to conformal symmetry, if the RG flow is irreversible, which is also in agreement with the c-theorem that roughly speaking says that the number of relevant degrees of freedom can not increase in the course of the RG flow (some kind of a second law of thermodynamics ...?). This means there can for example be no cyclic (limit point) behavior of the RG flow. By holographic considerations the author relates a cyclic behavior of the RG flow on the field theory side to inconistencies in the quantum gravity on the gravity side, which means that for certain systems scale invariance alone can not exist.

I do not well understand, why the RG flow has to be irreversible for the enhancement of scale invariance to conformal invariance in the first place. Is there a "direct" why how one could (and should ...) see this by only looking at the quantum field theory without making use of holographic arguments?

asked May 7, 2014 in Theoretical Physics by Dilaton (6,240 points) [ revision history ]
edited May 8, 2014 by Dilaton

Related http://www.physicsoverflow.org/6902/under-conditions-renormalization-group-equations-reversible

commented May 8, 2014 by Dilaton (6,240 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:
$\varnothing\hbar$ysicsOverflow
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

...