834 research outputs found
Noncommutative Gauge Theory on the q-Deformed Euclidean Plane
In this talk we recall some concepts of Noncommutative Gauge Theories. In
particular, we discuss the q-deformed two-dimensional Euclidean Plane which is
covariant with respect to the q-deformed Euclidean group. A Seiberg-Witten map
is constructed to express noncommutative fields in terms of their commutative
counterparts.Comment: 5 pages; Talk given by Frank Meyer at the 9th Adriatic Meeting,
September 4th-14th, 2003, Dubrovni
Noncommutative Geometry as a Regulator
We give a perturbative quantization of space-time in the case where the
commutators of the underlying algebra
generators are not central . We argue that this kind of quantum space-times can
be used as regulators for quantum field theories . In particular we show in the
case of the theory that by choosing appropriately the commutators
we can remove all the infinities by reproducing all the
counter terms . In other words the renormalized action on plus the
counter terms can be rewritten as only a renormalized action on the quantum
space-time . We conjecture therefore that renormalization of quantum
field theory is equivalent to the quantization of the underlying space-time
.Comment: Latex, 30 pages, no figures,typos corrected,references added .
Substantial amount of rewriting of the last section . Final interesting
remarks added at the end of the pape
Non-topological gravitating defects in five-dimensional anti-de Sitter space
A class of five-dimensional warped solutions is presented. The geometry is
everywhere regular and tends to five-dimensional anti-de Sitter space for large
absolute values of the bulk coordinate. The physical features of the solutions
change depending on the value of an integer parameter. In particular, a set of
solutions describes generalized gravitating kinks where the scalar field
interpolates between two different minima of the potential. The other category
of solutions describes instead gravitating defects where the scalar profile is
always finite and reaches the same constant asymptote both for positive and
negative values of the bulk coordinate. In this sense the profiles are
non-topological. The physical features of the zero modes are discussed.Comment: 9 pages, 4 figure
Non-renormalizability of noncommutative SU(2) gauge theory
We analyze the divergent part of the one-loop effective action for the
noncommutative SU(2) gauge theory coupled to the fermions in the fundamental
representation. We show that the divergencies in the 2-point and the 3-point
functions in the -linear order can be renormalized, while the
divergence in the 4-point fermionic function cannot.Comment: 15 pages, results presented at ESI 2d dilaton gravity worksho
Non-Commutative GUTs, Standard Model and C,P,T properties from Seiberg-Witten map
Noncommutative generalizations of Yang-Mills theories using Seiberg-Witten
map are in general not unique. We study these ambiguities and see that SO(10)
GUT, at first order in the noncommutativity parameter \theta, is unique and
therefore is a truly unified theory, while SU(5) is not. We then present the
noncommutative Standard Model compatible with SO(10) GUT. We next study the
reality, hermiticity and C,P,T properties of the Seiberg-Witten map and of
these noncommutative actions at all orders in \theta. This allows to compare
the Standard Model discussed in [5] with the present GUT inspired one.Comment: 9 pages. Presented at the Balkan Workshop 2003, Vrnjacka Banja,
29.8-2.9.2003 and at the 9th Adriatic Meeting, Dubrovnik, 4-14.9.200
On the first order operators in bimodules
We analyse the structure of the first order operators in bimodules introduced
by A. Connes. We apply this analysis to the theory of connections on bimodules
generalizing thereby several proposals.Comment: 13 pages, AMSLaTe
A note on the Deser-Tekin charges
Perturbed equations for an arbitrary metric theory of gravity in
dimensions are constructed in the vacuum of this theory. The nonlinear part
together with matter fields are a source for the linear part and are treated as
a total energy-momentum tensor. A generalized family of conserved currents
expressed through divergences of anti-symmetrical tensor densities
(superpotentials) linear in perturbations is constructed. The new family
generalizes the Deser and Tekin currents and superpotentials in quadratic
curvature gravity theories generating Killing charges in dS and AdS vacua. As
an example, the mass of the -dimensional Schwarzschild black hole in an
effective AdS spacetime (a solution in the Einstein-Gauss-Bonnet theory) is
examined.Comment: LATEX, 7 pages, no figure
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
On Coordinate Transformations in Planar Noncommutative Theories
We consider planar noncommutative theories such that the coordinates verify a
space-dependent commutation relation. We show that, in some special cases, new
coordinates may be introduced that have a constant commutator, and as a
consequence the construction of Field Theory models may be carried out by an
application of the standard Moyal approach in terms of the new coordinates. We
apply these ideas to the concrete example of a noncommutative plane with a
curved interface. We also show how to extend this method to more general
situations.Comment: 20 pages, 1 figure. references adde
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
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