• 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
5,054 questions , 2,207 unanswered
5,347 answers , 22,728 comments
1,470 users with positive rep
818 active unimported users
More ...

  Why holographic renormalization?

+ 5 like - 0 dislike

Why is there a need to perform holographic renormalization for the normal $AdS_5\times S^5$/CFT$_4$ correspondence if the brane theory is conformal? Since the flow along the AdS direction $r$ is related to the renormalization scale does this not explicitly introduce an "energy" parameter that breaks conformal invariance in the SYM side of the duality?

This post imported from StackExchange Physics at 2015-02-05 10:16 (UTC), posted by SE-user Marion
asked Jan 31, 2015 in Theoretical Physics by Marion Edualdo (250 points) [ no revision ]
retagged Feb 5, 2015
Hi @Marion. Consider adding references and links in order to receive useful and focused answers.

This post imported from StackExchange Physics at 2015-02-05 10:16 (UTC), posted by SE-user Qmechanic
Hi, thanks for the tip. The above question though I did not take it from a question out of a paper or so. It is my luck of understanding of the whole branch maybe.

This post imported from StackExchange Physics at 2015-02-05 10:16 (UTC), posted by SE-user Marion

1 Answer

+ 2 like - 0 dislike

The fact that the boundary theory is conformal means that renormalization does not induce running of the coupling. However, there are divergences which have to be regularized and renormalized. The regularization requires the introduction of an arbitrary scale, which is not Weyl invariant and leads to a conformal anomaly (in even dimensions).

Correspondingly, also the bulk theory has to be regularized by introducing a cutoff $\epsilon$ on the radial coordinate. The supergravity fields have to be expanded close to the horizon and local counterterms have to be introduced to subtract the divergences when taking the limit of $\epsilon\to 0$. For the metric, the regularization procedure requires picking a reference metric $g_{(0)}$ from the conformal structure on the boundary. For $d$ (boundary dimension) even, the dependence of the counterterm on the chosen reference metric leads to a renormalized Lagrangian, that is not Weyl invariant. One picks up exactly the expected Weyl anomaly.

This is a very neat example of a connection of boundary UV physics (the cutoff) and bulk IR physics (divergences close to the boundary) which lead to the same Weyl anomaly.

For details, see the paper by Henningson and Skenderis. There are also these very instructive lecture notes on holographic renormalization with the example of renormalization of the action of a massive bulk scalar.

This post imported from StackExchange Physics at 2015-02-05 10:16 (UTC), posted by SE-user physicus
answered Feb 5, 2015 by physicus (105 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:
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