Is Local Poincare Symmetry Exact in All Approaches to Quantum Gravity?

[JustinLevy]

It is my understanding that in string theory, loop quantum gravity, the 'asymptotic safety' approach, and in semiclassical quantum gravity, local Poincare symmetry is exact. But there are things like DSR (does the D stand for Deformed, or Doubly? I've heard people say it either way), which while not a quantum theory of gravity, do try to have poincare invariance in the low energy limit but have terms on the order of the Planck energy which violate poincare symmetry.

First, is this understanding correct? (are there any 'overview' papers which mention poincare symmetry explicitly which I could refer to?)

And second, can anyone list some examples of current mainstream approaches to quantum gravity that DO break local poincare symmetry? I am not aware of any.

If these approaches do exist, since the poincare group representations are usually used to identify particles in field theory, how do the theories deal with this now missing piece? Do they end up with anyons in addition to fermions and bosons?

 

[atyy]

The "condensed matter" approaches (Volovik; Visser; Wen; Horava) don't have exact Lorentz invariance. None of these work for gravity. However, the Levin and Wen review shows how matter in the form of QED and QCD might emerge from such a theory. Apparently this is related to the emergent gravity in AdS/CFT, which does have exact Lorentz invariance.

Wen
http://arxiv.org/abs/cond-mat/0407140
http://arxiv.org/abs/0907.1203

Visser
http://arxiv.org/abs/0909.5391

Volovik
http://books.google.com.sg/books?id=6uj76kFJOHEC&dq=volovik+universe&source=gbs_navlinks_s

Horava
http://arxiv.org/abs/0901.3775Group Field Theory, an approach related to LQG, gets matter that isn't Lorentz invariant
http://arxiv.org/abs/0912.2441
http://arxiv.org/abs/hep-th/0512113
http://arxiv.org/abs/0903.3475Steinacker's stuff is also interesting
http://arxiv.org/abs/0903.1015

 

[JustinLevy]

Oh wow! Thank you for collecting all those links.

It will take me quite awhile to work through all those; I've only read the abstracts so far. You comment that none of the first four work for gravity, but Horava seems to be presenting a theory of quantum gravity. Did I misunderstand your comment, or am I misunderstanding what Horava is trying to do?

Also, is my understanding correct that in string theory, loop quantum gravity, the 'asymptotic safety' approach, and in semiclassical quantum gravity, local Poincare symmetry is exact?

Thanks much.
The Volovik book's overview sounds really interesting. I'll check if the library has the older version in stock.

 

[atyy]

You comment that none of the first four work for gravity, but Horava seems to be presenting a theory of quantum gravity. Did I misunderstand your comment, or am I misunderstanding what Horava is trying to do?

If I remember the flaws of the first four are as follows:

Wen: gets massless graviton, but the dispersion relation is cubic; has a model where graviton may have a linear dispersion relation, but the calculation is unreliable and remains to be verified numerically

Volovik: massive graviton

Visser: gets modified Newtonian gravity

Horava: massless graviton but with extra scalar mode not consistent with observation (but some hope this may be tweaked into a feature that explains dark matter or something)

 

[atyy]

Another area to look at is the application of AdS/CFT ideas to non-relativistic physics, though here the theory is no longer UV complete:

http://arxiv.org/abs/0909.0518

 

[tom.stoer]

It is my understanding that in string theory, loop quantum gravity, the 'asymptotic safety' approach, and in semiclassical quantum gravity, local Poincare symmetry is exact. But there are things like DSR (does the D stand for Deformed, or Doubly? I've heard people say it either way), which while not a quantum theory of gravity, do try to have poincare invariance in the low energy limit but have terms on the order of the Planck energy which violate poincare symmetry.

D is both Doubly (because of a second fixed parameter) and Deformed. In DSR Poincare invariance is not broken but deformed and realized non-linearily, which results in the higher order terms.

Some time ago the LQG community speculated about DSR to be derived from LQG, but it became quiet about that. I am not sure if they are still thinking about it, but I guess this approach is a dead-end. Maybe it was an artefact of invalid approximations of a "semi-classical" state vector