Wednesday, December 06, 2006

Raman Sundrum: ghosts solving the cosmological constant

Raman Sundrum gave a very charming talk whose goal was to refine a crazy way to solve the cosmological constant problem.

Unbroken supersymmetry may explain why the vacuum energy is zero. But because we know that the supersymmetry must be broken, the predicted vacuum energy after SUSY breaking seems to be far too high, by 60 orders of magnitude. That's better than the 120 orders of magnitude at the beginning but it's still bad, a person who wants to promote a weird alternative to SUSY such as Raman would argue. Also, we know that what we want is a much smaller but nonzero vacuum energy.

His favorite models cancel the contributions of ordinary matter to the vacuum energy - from the zero energy of the harmonic oscillators, so to say - by a new kind of matter that has the same statistics but that has the opposite sign of the energy. The Standard Model as well as the ghost Standard Model preserve the Lorentz symmetry but they must be coupled via gravity and it is this gravitational sector that has to break the Lorentz symmetry for this picture to work, Raman concluded.

Some of the ghost gravity models he considers are called the Frank Einstein theory or Frankenstein theory for short. ;-)

In his most realistic models, he chooses a rather generic Lorentz-violating action for the gravity modes - or scalar modes in a toy model. The form factors are suppressed in the spatial dimensions - by "exp(-p^2)"-like factors - but not in the temporal dimension. That's more than enough to make the loop diagrams converge. The radiation modes of gravity remain relativistic in their essence while the other components of the metric tensor are converted to strange non-local fields analogous to fields associated with rigid balls that induce the action at a distance and whose propagators don't depend on the energy "p^0".

It is not clear to him what is the equation of state of the vacuum energy he generates and whether it could be compatible with observations. But he showed some pictures of inflation accompanied by a ghost inflation: ghost inflation occurs slightly earlier and the regular inflation dilutes the ghosts, too. If I remember well, the regular inflaton was one of the ghostbusters in this model. Ha ha ha ha ha ha.

All the active people in the room eventually agreed that it is not difficult to get rid of the UV divergences - even if we want to keep the Hilbert space positively definite - once we sacrifice Lorentz invariance. In fact, we get too much freedom if we allow these purely spatial form-factors. The resulting theory contains infinitely many parameters and is entirely unpredictive. According to my opinion, it is exactly as uninteresting as a generic non-renormalizable theory because it is the infinite set of unknowns that is the real problem, not the divergences.

Raman has also employed a spin-chain model with two types of excitations (ordinary, ghost) to argue that a model similar to his gravity model can emerge from a reasonable starting point. I was a bit confused by his ghost terminology because sometimes he meant modes of a positive norm and sometimes he didn't.

There has also been some discussion which of the models of massive and non-local gravity are morally or exactly equivalent to each other. It's a lot of fun to listen to free and powerful thinkers such as Raman. Nevertheless, you cannot avoid the feeling that the probability that something realistic or otherwise interesting comes out of a phenomenological model or framework is more or less directly proportional to the amount of string-theoretical concepts in this model or framework (extra dimensions, branes, bi-fundamental matter, etc.).

And Raman's current framework is not really close to string theory. ;-) Various assumptions about Nature or string theory can always turn out to be inaccurate, but I think that there exists no string-theoretical or other rational justification for the Lorentz symmetry breaking, ghosts, and other building blocks of these unusual theories.

The Hilbert spaces in all kinds of vacua we can imagine have the same natural boundedness of energy from below as the textbook consistent examples of quantum field theory. They also imply Lorentz symmetry in the UV. In perturbative string theory, one can show that closed string physics simply is Lorentz-invariant at distances shorter than the curvature scale of the background. Non-perturbatively, a similar statement probably holds, too. The Lorentz symmetry also has to reappear at very low energies because this is where it has been tested experimentally. There is not much room left in between. As far as I see, there is also no motivation - no known "profit" that we could make by "sacrificing" this nice symmetry.

Also, I don't see the point of looking for theories with finite loop diagrams if the constraints to build such theories are too loose because we end up with theories with infinitely many parameters which are unpredictive as explained above.

Renormalizable quantum field theories are an example of a nice equilibrium because the amount of different types of divergences agrees with the number of parameters of these theories. If you represent string theory as a worldsheet CFT or a boundary CFT or something else, the previous sentence is still essentially correct. The goal really can't be to remove divergences but to remove parameters.

Off-topic: the quality of search engines can be measured by looking how early you get really relevant answers to your queries. Yahoo has just gotten a little bit ahead of Google in physics searches: physics blog, string theory blog. Congratulations to Yahoo!

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