• 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 ...

  How local fields transform in the holographic boundary

+ 3 like - 0 dislike

Consider an holographic description of gravity $f:\Omega \rightarrow \partial \Omega$ such that gravitational fields and curvature in a neighbourhood $\Omega$ of 4D spacetime induce local fields on $\partial \Omega$. So if $G(\Omega)$ is a shorthand to describe all gravitational fields in the neighbourhood, then $g := f(G(\Omega))$ is a shorthand to describe all local fields in the holographic dual in $\partial \Omega$

I understand that we rarely have detailed information of the $f$ map. But usually one can ask questions about $f$ properties. In this case, I'm interested by the fact that for a given point $x$ in the spacetime, there are infinite neighbourhoods $\Omega$ such that $x \in \partial \Omega$

Question: what would you call the following property: Be $x$ a point in spacetime, and be $\Omega(x)$ a family of compact, simply connected sets such that if $\Omega \in \Omega(x)$ then $x \in \partial \Omega$. Assume that gravitational fields $G(\Omega)$ are defined everywhere on spacetime. Then the corresponding fields in the holographic dual $g:=f(G(\Omega)):\partial \Omega$ are such that if we take quantum field observable operators on $g$ and obtain vacuum expectation values of the operators around a small neighbourhood around $x$ with $x \in X_h$, then vacuum expectation values $\langle A_{g(\Omega)} \rangle_{X_h}$ of operators $A_g$ in the dual $g$ satisfy the following invariance property:

be $\Omega \in \Omega(x)$ and $\Omega' \in \Omega(x)$. Then $$ \langle A_{g(\Omega)} \rangle_{X_h} = \langle A_{g(\Omega')} \rangle_{X_h} $$

for $X_h$ small enough

This property seems to be intuitively some kind of condition that the holographic dual fields also behave as local fields in the embedding space. I'm not sure if it makes physical sense to demand it, but I'm trying to understand if it is an interesting property to demand from holographic duals. Naively I would be tempted to think that such invariance suggests that the holographic dual is a real physical field, in some sense


asked Jun 2, 2014 in Theoretical Physics by CharlesJQuarra (555 points) [ revision history ]
edited Jun 16, 2014 by CharlesJQuarra

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