128 research outputs found
Quantum canonical tensor model and an exact wave function
Tensor models in various forms are being studied as models of quantum
gravity. Among them the canonical tensor model has a canonical pair of
rank-three tensors as dynamical variables, and is a pure constraint system with
first-class constraints. The Poisson algebra of the first-class constraints has
structure functions, and provides an algebraically consistent way of
discretizing the Dirac first-class constraint algebra for general relativity.
This paper successfully formulates the Wheeler-DeWitt scheme of quantization of
the canonical tensor model; the ordering of operators in the constraints is
determined without ambiguity by imposing Hermiticity and covariance on the
constraints, and the commutation algebra of constraints takes essentially the
same from as the classical Poisson algebra, i.e. is first-class. Thus one could
consistently obtain, at least locally in the configuration space, wave
functions of "universe" by solving the partial differential equations
representing the constraints, i.e. the Wheeler-DeWitt equations for the quantum
canonical tensor model. The unique wave function for the simplest non-trivial
case is exactly and globally obtained. Although this case is far from being
realistic, the wave function has a few physically interesting features; it
shows that locality is favored, and that there exists a locus of configurations
with features of beginning of universe.Comment: 17 pages. Section 2 expanded to include fuzzy-space interpretation,
and other minor change
Low-energy propagation modes on string network
We study low-energy propagation modes on string network lattice.
Specifically, we consider an infinite two-dimensional regular hexagonal string
network and analyze the low frequency propagation modes on it. The fluctuation
modes tangent to the two-dimensional plane respect the spatial rotational
symmetry on the plane, and are described by Maxwell theory. The gauge symmetry
comes from the marginal deformation of changing the sizes of the loops of the
lattice. The effective Lorentz symmetry respected at low energy will be
violated at high energy.Comment: LaTeX, 10 pages, 3 figures, a wrong factor correcte
Emergent general relativity in the tensor models possessing Gaussian classical solutions
This paper gives a summary of the author's works concerning the emergent
general relativity in a particular class of tensor models, which possess
Gaussian classical solutions. In general, a classical solution in a tensor
model may be physically regarded as a background space, and small fluctuations
about the solution as emergent fields on the space. The numerical analyses of
the tensor models possessing Gaussian classical background solutions have shown
that the low-lying long-wavelength fluctuations around the backgrounds are in
one-to-one correspondence with the geometric fluctuations on flat spaces in the
general relativity. It has also been shown that part of the orthogonal symmetry
of the tensor model spontaneously broken by the backgrounds can be identified
with the local translation symmetry of the general relativity. Thus the tensor
model provides an interesting model of simultaneous emergence of space, the
general relativity, and its local gauge symmetry of translation.Comment: 15pages, 5 figures, based on the proceedings of VIII International
Workshop, "Lie Theory and its Applications in Physics", Varna, 15 - 21 June
2009, and of XXV Max Born Symposium, ``The Planck Scale'', Wroclaw, 29 June -
3 July 200
Gauge fixing in the tensor model and emergence of local gauge symmetries
The tensor model can be regarded as theory of dynamical fuzzy spaces, and
gives a way to formulate gravity on fuzzy spaces. It has recently been shown
that the low-lying fluctuations around the Gaussian background solutions in the
tensor model agree correctly with the metric fluctuations on the flat spaces
with general dimensions in the general relativity. This suggests that the local
gauge symmetry (the symmetry of local translations) is also emergent around
these solutions. To systematically study this possibility, I apply the BRS
gauge fixing procedure to the tensor model. The ghost kinetic term is
numerically analyzed, and it has been found that there exist some massless
trajectories of ghost modes, which are clearly separated from the other higher
ghost modes. Comparing with the corresponding BRS gauge fixing in the general
relativity, these ghost modes forming the massless trajectories in the tensor
model are shown to be identical to the reparametrization ghosts in the general
relativity.Comment: 18 pages, 5 figure
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