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MTd2

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The abstract of the new Sotiriou-Visser-Weinfurtner paper sounds pretty explosive:

Because causal dynamical triangulations slices up spacetime into surfaces of "constant time", I'd always worried that it was quantizing not general relativity but some other theory - one that has a built-in separation between time and space. Hořava-Lifgarbagez gravity is such a theory. Wikipedia writes:MTd2 said:We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can fully reproduce the behaviour of the latter in this regime. In particular, we show that Hořava-Lifgarbagez gravity can mimic the flow of the spectral dimension in causal dynamical triangulations to high accuracy and over a wide range of scales. This seems to indicate that the two theories lie in the same universality class.

Hořava-Lifgarbagez gravity (or Hořava gravity) is a theory of quantum gravity proposed by Petr Hořava in 2009. It solves the problem of different concepts of time in quantum field theory and general relativity by treating the quantum concept as the more fundamental so that space and time are not equivalent (anisotropic). The relativistic concept of time with its Lorentz invariance emerges at large distances. The theory relies on the theory of foliations to produce its causal structure. It is related to topologically massive gravity and the Cotton tensor. It is a possible UV completion of general relativity. The novelty of this approach, compared to previous approaches to quantum gravity such as Loop quantum gravity, is that it uses concepts from condensed matter physics such as quantum critical phenomena.

Hořava's initial formulation was found to have side-effects such as predicting very different results for a spherical Sun compared to a slightly non-spherical Sun, so others have modified the theory. Inconsistencies remain.

How are the causal dynamical triangulations people reacting to the work of Sotiriou, Visser, and Weinfurtner? Do they agree that they may be quantizing Hořava-Lifgarbagez gravity?

I haven't been paying attention to this stuff, but I may find out the answer to this question when I go to Zurich tonight. I guess both Ambjorn and Loll will be there.

By the way, your posts listing these abstracts serve as a nice quick way to catch up on recent work in quantum gravity. Thanks! I don't want to seem like I'm completely out of the loop.

Hmm, here's what Ambjorn and Loll say in their new review article:

What is curious about the phase structure of four-dimensional CDT quantum gravity is its resemblance with that of Horava-Lifgarbagez gravity [17], which has been spelled out further in [18,19]. It gives rise to the intriguing conjecture that there may be a universal phase diagram governing systems of higher-dimensional, dynamical geometry, and accomodating a variety of gravity theories, some of which may be anisotropic in space and time.

To someone raised on relativity it would seem a painful step to admit one is quantizing a theory where there really is a single "right" notion of time, and Lorentz transformations are just a kind of approximate symmetry, good at macroscopic scales. Maybe they hope they can get at quantum general relativity as one point in the phase diagram of Horava-Lifgarbagez theories.