• 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.


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

126 submissions , 106 unreviewed
3,683 questions , 1,271 unanswered
4,657 answers , 19,740 comments
1,470 users with positive rep
442 active unimported users
More ...

6d Massive Gravity

+ 12 like - 0 dislike

Massive gravity (with a Fierz-Pauli mass) in 4 dimensions is very well-studied, involving exotic phenomena like the vDVZ discontinuity and the Vainshtein effect that all have an elegant and physically transparent explanation in terms of an effective field theory of longitudinal modes, as explained by Arkani-Hamed, Georgi, and Schwartz. Is there any analogous work on six-dimensional massive gravity? (The right mass term would still be of Fierz-Pauli form, but the little group is bigger and so I would expect a more complicated set of longitudinal modes to think about.)

EDIT: added a bounty to renew interest.

This post has been migrated from (A51.SE)
asked Sep 24, 2011 in Theoretical Physics by Matt Reece (1,630 points) [ no revision ]
retagged Mar 18, 2014 by dimension10
I am not sure if this is helpful, but 1010.0494 and 0902.0981 have good reviews of spinor helicity in six dimensions, which may help in efficient organization of the problem.

This post has been migrated from (A51.SE)

1 Answer

+ 4 like - 0 dislike

Unfortunately I am not really aware of any literature regarding this, however a generalization of the Arkani-Hamed et al paper to the case of d+1 dimensions should be rather straightforward.

Let us begin by noting a few basic facts about the group theory involved: The little group for a massless representation (this is the analog of helicity) of the Poincaré algebra is given by $SO(d-2)$, while the little group for a massive representation is given by $SO(d-1)$. The number of degrees of freedom corresponding to massive spin-2 is given by the symmetric traceless tensor of the little group, which has $\frac{d(d+1)}{2} -1$ degrees of freedom. In the massless case a similar argument leads to $\frac{(d-1)d}{2}-1$.

Now the point of the analysis by Arkani-Hamed et al is essentially to understand the theory in the UV, i.e. at energy scales much larger than the mass. To do this they try to decompose the massive representation in terms of massless ones, a straightforward counting exercise shows that in this case a massive spin-2 decomposes into a scalar, a helicity-1 vector and a helicity-2, exactly as in the 3+1d case. Using this knowledge it should be very easy to generalize the previous results, it is mostly a matter of carefully keeping track of the $d$'s. The vDVZ discontinuity, will still be there although the relative factor in the radiation-radiation and matter-matter interaction will depend on d, this can easily be seen by decomposing the tensor structure of the massive spin-2 propagator in terms of three massless one's corresponding to the helicities, a nice derivation for the $d=3$ case can be found in Zee's QFT book.

I hope that helps a bit...

This post has been migrated from (A51.SE)
answered Nov 3, 2011 by user558 (40 points) [ no revision ]
Right, this much I had reasoned through already. But there's also a more complicated set of helicity states that could appear in the scattering amplitudes; e.g., the (Stückelberged-in, massless) vector part now transforms under $SO(4) \sim SU(2) \times SU(2)$, so one can consider scattering of a state carrying helicity $\pm 1$ under the first SU(2) factor with states carrying helicity $\pm 1$ under the second, and so on. It should be straightforward; I was just wondering if any reference has already worked it out. Thanks, though.

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).
To avoid this verification in future, please log in or register.

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights