207 research outputs found
Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces,
because a fuzzy space is defined by a three-index coefficient of the product
between functions on it, f_a*f_b=C_ab^cf_c. In this paper, this previous
proposal is applied to dynamical generation of commutative nonassociative fuzzy
spaces. It is numerically shown that fuzzy flat torus and fuzzy spheres of
various dimensions are classical solutions of the rank-three tensor model.
Since these solutions are obtained for the same coupling constants of the
tensor model, the cosmological constant and the dimensions are not fundamental
but can be regarded as dynamical quantities. The symmetry of the model under
the general linear transformation can be identified with a fuzzy analog of the
general coordinate transformation symmetry in general relativity. This symmetry
of the tensor model is broken at the classical solutions. This feature may make
the model to be a concrete finite setting for applying the old idea of
obtaining gravity as Nambu-Goldstone fields of the spontaneous breaking of the
local translational symmetry.Comment: Adding discussions on effective geometry, a note added, four
references added, other minor changes, 27 pages, 17 figure
A Note on String Field Theory in the Temporal Gauge
In this note, we review the recent developments in the string field theory in
the temporal gauge. (Based on a talk presented by N.I. in the workshop {\it
Quantum Field Theory, Integrable Models and Beyond}, Yukawa Institute for
Theoretical Physics, Kyoto University, 14-18 February 1994.)Comment: 20 pages, KEK-TH-411, LaTex fil
Field theory on evolving fuzzy two-sphere
I construct field theory on an evolving fuzzy two-sphere, which is based on
the idea of evolving non-commutative worlds of the previous paper. The
equations of motion are similar to the one that can be obtained by dropping the
time-derivative term of the equation derived some time ago by Banks, Peskin and
Susskind for pure-into-mixed-state evolutions. The equations do not contain an
explicit time, and therefore follow the spirit of the Wheeler-de Witt equation.
The basic properties of field theory such as action, gauge invariance and
charge and momentum conservation are studied. The continuum limit of the scalar
field theory shows that the background geometry of the corresponding continuum
theory is given by ds^2 = -dt^2+ t d Omega^2, which saturates locally the
cosmic holographic principle.Comment: Typos corrected, minor changes, 23 pages, no figures, LaTe
An invariant approach to dynamical fuzzy spaces with a three-index variable
A dynamical fuzzy space might be described by a three-index variable
C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c among
the functions f_a on the fuzzy space. A fuzzy analogue of the general
coordinate transformation would be given by the general linear transformation
on f_a. I study equations for the three-index variable invariant under the
general linear transformation, and show that the solutions can be generally
constructed from the invariant tensors of Lie groups. As specific examples, I
study SO(3) symmetric solutions, and discuss the construction of a scalar field
theory on a fuzzy two-sphere within this framework.Comment: Typos corrected, 12 pages, 8 figures, LaTeX, JHEP clas
Heat kernel, effective action and anomalies in noncommutative theories
Being motivated by physical applications (as the phi^4 model) we calculate
the heat kernel coefficients for generalised Laplacians on the Moyal plane
containing both left and right multiplications. We found both star-local and
star-nonlocal terms. By using these results we calculate the large mass and
strong noncommutativity expansion of the effective action and of the vacuum
energy. We also study the axial anomaly in the models with gauge fields acting
on fermions from the left and from the right.Comment: 21 pages, v2: references adde
Wightman function and vacuum densities for a Z_2-symmetric thick brane in AdS spacetime
Positive frequency Wightman function, vacuum expectation values of the field
square and the energy-momentum tensor induced by a Z_{2}-symmetric brane with
finite thickness located on (D+1)- dimensional AdS background are evaluated for
a massive scalar field with general curvature coupling parameter. For the
general case of static plane symmetric interior structure the expectation
values in the region outside the brane are presented as the sum of free AdS and
brane induced parts. For a conformally coupled massless scalar the brane
induced part in the vacuum energy-momentum tensor vanishes. In the limit of
strong gravitational fields the brane induced parts are exponentially
suppressed for points not too close to the brane boundary. As an application of
general results a special model is considered in which the geometry inside the
brane is a slice of the Minkowski spacetime orbifolded along the direction
perpendicular to the brane. For this model the Wightman function, vacuum
expectation values of the field square and the energy-momentum tensor inside
the brane are evaluated as well and their behavior is discussed in various
asymptotic regions of the parameters. It is shown that for both minimally and
conformally coupled scalar fields the interior vacuum forces acting on the
brane boundaries tend to decrease the brane thickness.Comment: 25 pages, 6 figures, discussion adde
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