• 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
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Interplay between the cosmological constant and "microscopic" properties of string vacua

+ 4 like - 0 dislike

As far as I understand, string phenomenology is usually concerned with compactifications of string theory, M-theory or F-theory in which the uncompactified dimensions form a 4-dimensional Minkowski spacetime. However, we know our actual universe has a positive cosmological constant hence its asymptotics are that of a De Sitter spacetime. On the intuitive level it makes sense to me, since the microscopic physics should have little to do with spacetime asymptotics. However, from another point of view I see a problem.

It seems to me that a cosmological constant in the effective 4-dimensional field theory requires a non-vanishing Ricci tensor in the compactified dimensions. For example, the classical case study for anti-De Sitter string theory is AdS_4 x S_6. The compactified dimensions form the sphere, a manifold with positive curvature, compensating the negative curvature of AdS.

This non-vanishing Ricci tensor seems to require different topology from a vanishing Ricci tensor. Hence all standard compactifications like Calabi-Yau manifolds, G2 manifolds etc. don't seem to be compatible with a non-vanishing cosmological constant.

What am I missing here?

This post has been migrated from (A51.SE)
asked Dec 11, 2011 in Theoretical Physics by Squark (1,725 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

First of all, in the most recent decade, string phenomenology isn't talking about strictly Minkowski vacua. E.g. in the KKLT paper, you will see $AdS_4$ vacua uplifted to $dS_4$ by antibranes and no Minkowski space at any place in between.

The fact that a nonzero C.C. is generated for the large 3+1 dimensions doesn't mean that one can't find any shape of the hidden dimensions that exactly obey the equations of motion. Just like there exists a "tiny C.C." deformation of the flat Minkowski space, namely the $dS_4$ space with a small C.C. around us, there also exist solutions for the compact 6/7 dimensions that have a tiny (but nonzero) Ricci tensor proportional to the Ricci scalar. In the Calabi-Yau case, these deformed solutions will strictly no longer be $SU(3)$ holonomy manifolds; they will be $U(3)$ holonomy (Kähler) manifolds if we acknowledge that the Ricci curvature, while tiny, is nonzero.

In braneworld compactifications and compactifications on singular compactified manifolds, the energy density is typically concentrated at the loci of the branes or the singularities.

This post has been migrated from (A51.SE)
answered Dec 12, 2011 by Luboš Motl (10,278 points) [ no revision ]
I see. Is it true, though, that the introduction of a positive C.C. eliminates at least some of the Minkowski sectors? I.e. not all such sectors can be deformed to something with positive C.C. ?

This post has been migrated from (A51.SE)
Dear @Squark, I don't know. I am not aware of an example of such an obstruction. Don't forget that the cosmological constant is just some vacuum energy (and momentum). The presence of generic nonzero stress-energy tensor can't invalidate the existence of hidden dimensions with a topology. If this were the case, no matter could ever propagate in the hidden dimensions because matter carries some stress-energy tensor, too, not just the vacuum energy. The background just "backreacts" and adjusts itself to whatever you insert, and if the inserted stress-energy tensor is tiny, it's not a problem.

This post has been migrated from (A51.SE)
Dear @Lubos, my intuition here is coming from compact 2 dimensional manifolds where the integral of the curvature over the surface is determined solely by the topology

This post has been migrated from (A51.SE)

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