Quantcast
  • 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.

News

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

Attributions

(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 ...

  Temperature in CFT

+ 3 like - 0 dislike
2461 views

Non-vanishing Temperature can break conformal symmetry(Can anyone show this point explicitly), my question is that in AdS/CFT the temperature of boundary field theory is non-zero, why the boundary field theory whose conformal symmetry is breaking is still a conformal field theory?

This post imported from StackExchange Physics at 2014-10-20 10:36 (UTC), posted by SE-user Yuan Sun
asked Oct 20, 2014 in Theoretical Physics by Yuan Sun (15 points) [ no revision ]

Non-vanishing temperature already breaks Lorentz symmetry as the concept of temperature requires a distinguished time direction. However, only the state has the broken symmetry, not the theory itself. This should answer your second question, too.

 I am not being very clear about " only the state has the broken symmetry, not the theory itself." Could you give more comment about this? 

I read the followings just now in Freedman's book "Supergravity" (Page 528) which is helpful.

"If the gravity solution is pure AdS$_{d+1}$, these correlators are covariant under conformal transformations. If the bulk solution looks like AdS$_{d+1}$ near the boundary but differs in the interior, then conformal symmetry is broken. The boundary data can then act as sources for operators, which perturb a conformal theory and induce renormalization group flows. An alternative is that conformal symmetry is broken by non-vanishing onepoint functions <O(x)>, which indicate that the boundary CFT$_d$ is not in its ground state.If the bulk spacetime includes a black hole with non-zero Hawking temperature, then the gravity dual is a CFT in a thermal ensemble."

"only the state has the broken symmetry, not the theory itself". This means that even for a conformal theory whose ground state has the full conformal symmetry, nevertheless all thermal states have (necessarily) broken Lorentz (and hence conformal) symmetry. The expectations are taken with respect to the thermal (KMS) state, and because of the broken symmetry, a vector operator can have a non-vanishing one-point function.

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:
$\varnothing\hbar$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
...