• 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
5,075 questions , 2,226 unanswered
5,348 answers , 22,757 comments
1,470 users with positive rep
818 active unimported users
More ...

  Why are holomorphic boundary CFT2 primary operators massless in the AdS3 bulk?

+ 5 like - 0 dislike

I saw a claim in this paper that holomorphic boundary CFT$_2$ primary operators correspond to massless states in the AdS$_3$ bulk. Specifically,

As always, we simplify the situation by assuming the absence of holomorphic primary operators. (These would have a little group different from that of a massive particle in the bulk of AdS; therefore for small $\Lambda = −L^{-2}$ they can only correspond to massless states, which do not have a rest frame, or else to states which do not propagate into the bulk of AdS at all.)

My question is: how did he arrive at this conclusion/where can I find an explanation? I can't figure it out, and nowhere near the claim does he give any relevant sources. It's certainly conceivable: holomorphic primary operators will include gauge fields, for example.

This post imported from StackExchange Physics at 2014-06-13 12:28 (UCT), posted by SE-user wittensdog
asked Apr 3, 2014 in Theoretical Physics by wittensdog (45 points) [ no revision ]
Minor comment to the post (v2): In the future please link to abstract pages rather than pdf files, e.g., arxiv.org/abs/0902.2790

This post imported from StackExchange Physics at 2014-06-13 12:28 (UCT), posted by SE-user Qmechanic

1 Answer

+ 0 like - 0 dislike

Unitarity of the CFT imposes a lower bound on the conformal dimension $\Delta $ of any operator as is stated in page 32 : $$ \Delta \geq \frac{d-2} 2 $$ My guess is that for this case since $ d=2 $ we have $\Delta_{equality}=0 $ which corresponds to the primary operator and assuming the field is scalar this corresponds to $ m=0 $ in the AdS bulk

Does this help in any way? I'm no expert here.

This post imported from StackExchange Physics at 2014-06-13 12:28 (UCT), posted by SE-user atabler
answered May 6, 2014 by atabler (0 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