Gregory Gabadadze & UV Lorentz violations

Gregory Gabadadze was just speaking about the infrared modifications of gravity, one of his recent favorite topics. This includes various theories of massive gravity and spontaneous Lorentz symmetry breaking. In the latter case, for example, they found theories

• hep-th/0412232
  

in which the massive graviton only has two polarizations. This can only occur because there is neither Lorentz symmetry nor Galilean symmetry using which you could go to its rest frame in such a way that the rotational symmetry would be preserved: if it were preserved, the spin "j=2" particle would have to have "(2j+1)=5" polarizations.

There has been a discussion about the Lorentz symmetry restoration in the UV. One may imagine that the diffeomorphism symmetry group is always preserved - even Newton's theory may be written in a diff invariant fashion - but the real physical issue is whether the spontaneous Lorentz symmetry breaking is undone at high energies.

In normal theories where you break the Lorentz symmetry spontaneously - e.g. by Coke in a bottle - the original causality (the speed limit "v less than c") is guaranteed to be preserved. This is a consequence of the Lorentz symmetry restoration in the UV regime. However, one may construct theories - at least UV incomplete theories - that violate this property. I am a bit uncertain whether such theories that allow the Lorentz symmetry to be broken spontaneously in the deep UV may be UV-consistent.




The examples from string theory tell us a pretty simple story. For example, the B-field inside the D-branes introduces non-commutativity and it breaks the Lorentz/rotational symmetry spontaneously. But the speed of gravity waves (closed strings) remains the ultimate restriction. The open string modes propagating inside the D-branes may be forced to move more slowly...

There were many other papers discussed in his talk, but right now I don't have time and energy to describe it here.