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Emergent Gravity at a Lifgarbagez Point from a Bose Liquid on the Lattice

Cenke Xu, Petr Horava

(Submitted on 1 Mar 2010)

We propose a model with quantum bosons on the fcc lattice, which has a stable algebraic Bose liquid phase at low energy. We show that this phase is described by emergent quantum gravity at the Gaussian z = 3 Lifgarbagez fixed point in 3+1 dimensions. The stability of this algebraic Bose liquid phase is guaranteed by the gauge symmetry of gravitons and self-duality of the low energy field theory. By tuning one parameter in the lattice boson model we can drive a phase transition between the z = 3 Lifgarbagez gravity and another algebraic Bose liquid phase, described by gravity at the z = 2 Lifgarbagez point

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"It should be noted that there are two distinct ways in which one can attempt to relate Lifgarbagez gravity to lattice models. In this paper, we work on a fixed rigid lattice, and find degrees of freedom whose long distance dynamics is captured by the Gaussian fixed points of Lifgarbagez gravity. The lattice is nondynamical. Alternatively, one can try to obtain Lifgarbagez gravity as a continuum limit of a lattice model defined as a sum over a suitable class of random triangulations of spacetime geometries. Here it is the lattice itself that is dynamical, and no extra degrees of freedom are invoked.The most promising candidate for such a random lattice model is offered by the causal dynamical triangulations (CDT) approach to quantum gravity.In the CDT approach (see Ref. [7] for a review), a summation over random lattices constrained to respect a preferred foliation structure of spacetime serves as a nonperturbative definition of quantum gravity, and yields a continuum limit with four macroscopic spacetime dimensions at long distances. It has been suggested in [8] (see also the recent paper [9]) that the CDT approach might be viewed as a lattice regularization of Lifgarbagez gravity. Further evidence for this scenario comes from the qualitative behavior of the spectral dimension of spacetime, which indicates that the model flows from a z = 3 UV fixed point to an z = 1 fixed point at long distances [8]."

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"Since the full nonlinear Lifgarbagez gravity of [1, 2] does not require a choice of a preferred flat background, it is natural to speculate that attempts to turn on the self-interaction of

gravitons in our lattice framework may ask for the underlying lattice itself to become dynamical. We will leave these topics to future studies."

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# Petr Horava hints he is going to work with CDT!

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