964 research outputs found
Tensor models and hierarchy of n-ary algebras
Tensor models are generalization of matrix models, and are studied as models
of quantum gravity. It is shown that the symmetry of the rank-three tensor
models is generated by a hierarchy of n-ary algebras starting from the usual
commutator, and the 3-ary algebra symmetry reported in the previous paper is
just a single sector of the whole structure. The condition for the Leibnitz
rules of the n-ary algebras is discussed from the perspective of the invariance
of the underlying algebra under the n-ary transformations. It is shown that the
n-ary transformations which keep the underlying algebraic structure invariant
form closed finite n-ary Lie subalgebras. It is also shown that, in physical
settings, the 3-ary transformation practically generates only local
infinitesimal symmetry transformations, and the other more non-local
infinitesimal symmetry transformations of the tensor models are generated by
higher n-ary transformations.Comment: 13 pages, some references updated and correcte
Uniqueness of canonical tensor model with local time
Canonical formalism of the rank-three tensor model has recently been
proposed, in which "local" time is consistently incorporated by a set of first
class constraints. By brute-force analysis, this paper shows that there exist
only two forms of a Hamiltonian constraint which satisfies the following
assumptions: (i) A Hamiltonian constraint has one index. (ii) The kinematical
symmetry is given by an orthogonal group. (iii) A consistent first class
constraint algebra is formed by a Hamiltonian constraint and the generators of
the kinematical symmetry. (iv) A Hamiltonian constraint is invariant under time
reversal transformation. (v) A Hamiltonian constraint is an at most cubic
polynomial function of canonical variables. (vi) There are no disconnected
terms in a constraint algebra. The two forms are the same except for a slight
difference in index contractions. The Hamiltonian constraint which was obtained
in the previous paper and behaved oddly under time reversal symmetry can
actually be transformed to one of them by a canonical change of variables. The
two-fold uniqueness is shown up to the potential ambiguity of adding terms
which vanish in the limit of pure gravitational physics.Comment: 21 pages, 12 figures. The final result unchanged. Section 5 rewritten
for clearer discussions. The range of uniqueness commented in the final
section. Some other minor correction
The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity
Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this
paper, I study numerically the fluctuation spectra around a Gaussian classical
solution of a tensor model, which represents a fuzzy flat space in arbitrary
dimensions. It is found that the momentum distribution of the low-lying
low-momentum spectra is in agreement with that of the metric tensor modulo the
general coordinate transformation in the general relativity at least in the
dimensions studied numerically, i.e. one to four dimensions. This result
suggests that the effective field theory around the solution is described in a
similar manner as the general relativity.Comment: 29 pages, 13 figure
The lowest modes around Gaussian solutions of tensor models and the general relativity
In the previous paper, the number distribution of the low-lying spectra
around Gaussian solutions representing various dimensional fuzzy tori of a
tensor model was numerically shown to be in accordance with the general
relativity on tori. In this paper, I perform more detailed numerical analysis
of the properties of the modes for two-dimensional fuzzy tori, and obtain
conclusive evidences for the agreement. Under a proposed correspondence between
the rank-three tensor in tensor models and the metric tensor in the general
relativity, conclusive agreement is obtained between the profiles of the
low-lying modes in a tensor model and the metric modes transverse to the
general coordinate transformation. Moreover, the low-lying modes are shown to
be well on a massless trajectory with quartic momentum dependence in the tensor
model. This is in agreement with that the lowest momentum dependence of metric
fluctuations in the general relativity will come from the R^2-term, since the
R-term is topological in two dimensions. These evidences support the idea that
the low-lying low-momentum dynamics around the Gaussian solutions of tensor
models is described by the general relativity. I also propose a renormalization
procedure for tensor models. A classical application of the procedure makes the
patterns of the low-lying spectra drastically clearer, and suggests also the
existence of massive trajectories.Comment: 31 pages, 8 figures, Added references, minor corrections, a
misleading figure replace
Matrix models and QCD with chemical potential
The Random Matrix Model approach to Quantum Chromodynamics (QCD) with non-vanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral Perturbation Theory (echPT). Two types of Matrix Model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with echPT. All known analytic results for the spectrum of complex and symplectic Matrix Models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent Lattice simulations are also discussed
Gauge field theories with covariant star-product
A noncommutative gauge theory is developed using a covariant star-product
between differential forms defined on a symplectic manifold, considered as the
space-time. It is proven that the field strength two-form is gauge covariant
and satisfies a deformed Bianchi identity. The noncommutative Yang-Mills action
is defined using a gauge covariant metric on the space-time and its gauge
invariance is proven up to the second order in the noncommutativity parameter.Comment: Dedicated to Ioan Gottlieb on the occasion of his 80th birthday
anniversary. 12 page
A renormalization procedure for tensor models and scalar-tensor theories of gravity
Tensor models are more-index generalizations of the so-called matrix models,
and provide models of quantum gravity with the idea that spaces and general
relativity are emergent phenomena. In this paper, a renormalization procedure
for the tensor models whose dynamical variable is a totally symmetric real
three-tensor is discussed. It is proven that configurations with certain
Gaussian forms are the attractors of the three-tensor under the renormalization
procedure. Since these Gaussian configurations are parameterized by a scalar
and a symmetric two-tensor, it is argued that, in general situations, the
infrared dynamics of the tensor models should be described by scalar-tensor
theories of gravity.Comment: 20 pages, 3 figures, references added, minor correction
Phonon Dynamics and Multipolar Isomorphic Transition in beta-pyrochlore KOs2O6
We investigate with a microscopic model anharmonic K-cation oscillation
observed by neutron experiments in beta-pyrochlore superconductor KOs2O6, which
also shows a mysterious first-order structural transition at Tp=7.5 K. We have
identified a set of microscopic model parameters that successfully reproduce
the observed temperature dependence and the superconducting transition
temperature. Considering changes in the parameters at Tp, we can explain
puzzling experimental results about electron-phonon coupling and neutron data.
Our analysis demonstrates that the first-order transition is multipolar
transition driven by the octupolar component of K-cation oscillations. The
octupole moment does not change the symmetry and is characteristic to
noncentrosymmetric K-cation potential.Comment: 5 pages, 4 figures, submitted to J. Phys. Soc. Jp
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