378 research outputs found
New Fuzzy Extra Dimensions from Gauge Theories
We start with an Yang-Mills theory on a manifold ,
suitably coupled to two distinct set of scalar fields in the adjoint
representation of , which are forming a doublet and a triplet,
respectively under a global symmetry. We show that a direct sum of
fuzzy spheres emerges as the vacuum solution after the spontaneous breaking of the
gauge symmetry and lay the way for us to interpret the spontaneously broken
model as a gauge theory over . Focusing
on a gauge theory we present complete parameterizations of the
-equivariant, scalar, spinor and vector fields characterizing the
effective low energy features of this model. Next, we direct our attention to
the monopole bundles over with winding numbers ,
which naturally come forth through certain projections of , and
discuss the low energy behaviour of the gauge theory over . We study models with -component multiplet of the
global , give their vacuum solutions and obtain a class of winding
number monopole bundles as certain
projections of these vacuum solutions. We make the observation that is indeed the bosonic part of the fuzzy supersphere with
supersymmetry and construct the generators of the Lie superalgebra
in two of its irreducible representations using the matrix content of the
vacuum solution . Finally, we show that our vacuum solutions
are stable by demonstrating that they form mixed states with non-zero von
Neumann entropy.Comment: 27+1 pages, revised version, added references and corrected typo
Equivariant Fields in an Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
We find new spontaneously generated fuzzy extra dimensions emerging from a
certain deformation of supersymmetric Yang-Mills (SYM) theory with cubic
soft supersymmetry breaking and mass deformation terms. First, we determine a
particular four dimensional fuzzy vacuum that may be expressed in terms of a
direct sum of product of two fuzzy spheres, and denote it in short as . The direct sum structure of the vacuum is revealed
by a suitable splitting of the scalar fields in the model in a manner that
generalizes our approach in \cite{Seckinson}. Fluctuations around this vacuum
have the structure of gauge fields over ,
and this enables us to conjecture the spontaneous broken model as an effective
gauge theory on the product manifold . We support this interpretation by
examining the theory and determining all of the
equivariant fields in the model, characterizing its low energy degrees of
freedom. Monopole sectors with winding numbers are accessed from after suitable projections and subsequently equivariant fields in these
sectors are obtained. We indicate how Abelian Higgs type models with vortex
solutions emerge after dimensionally reducing over the fuzzy monopole sectors
as well. A family of fuzzy vacua is determined by giving a systematic treatment
for the splitting of the scalar fields and it is made manifest that suitable
projections of these vacuum solutions yield all higher winding number fuzzy
monopole sectors. We observe that the vacuum configuration identifies with the bosonic part of the product of two fuzzy
superspheres with supersymmetry and elaborate on this
feature.Comment: 38+1 pages, published versio
A Gauge Theory on Fuzzy Extra Dimensions
In this article, we explore the low energy structure of a gauge theory
over spaces with fuzzy sphere(s) as extra dimensions. In particular, we
determine the equivariant parametrization of the gauge fields, which transform
either invariantly or as vectors under the combined action of rotations
of the fuzzy spheres and those gauge transformations generated by carrying the spin irreducible representation of . The
cases of a single fuzzy sphere and a particular direct sum of
concentric fuzzy spheres, , covering the monopole bundle
sectors with windings are treated in full and the low energy degrees of
freedom for the gauge fields are obtained. Employing the parametrizations of
the fields in the former case, we determine a low energy action by tracing over
the fuzzy sphere and show that the emerging model is abelian Higgs type with
gauge symmetry and possess vortex solutions on , which we discuss in some detail. Generalization of our formulation to
the equivariant parametrization of gauge fields in theories is also
briefly addressed.Comment: 27+1 page
Magnetic Field and Curvature Effects on Pair Production II: Vectors and Implications for Chromodynamics
We calculate the pair production rates for spin- or vector particles on
spaces of the form with corresponding to
(flat), (positive curvature) and (negative
curvature), with and without a background (chromo)magnetic field on . Beyond
highlighting the effects of curvature and background magnetic field, this is
particularly interesting since vector particles are known to suffer from the
Nielsen-Olesen instability, which can dramatically increase pair production
rates. The form of this instability for and is obtained. We also
give a brief discussion of how our results relate to ideas about confinement in
nonabelian theories.Comment: 24 pages, 9 figure
Magnetic Field and Curvature Effects on Pair Production I: Scalars and Spinors
The pair production rates for spin-zero and spin- particles are
calculated on spaces of the form with
corresponding to (flat), (flat, compactified),
(positive curvature) and (negative curvature), with and without a
background magnetic field on . The motivation is to elucidate the effects of
curvature and background magnetic field. Contrasting effects for positive and
negative curvature on the two cases of spin are obtained. For positive
curvature, we find enhancement for spin-zero and suppression for
spin-, with the opposite effect for negative curvature.Comment: 28 pages, 10 figure
Mesencephalon; Midbrain
The mesencephalon is the most rostral part of the brainstem and sits above the pons and is adjoined rostrally to the thalamus. It comprises two lateral halves, called the cerebral peduncles; which is again divided into an anterior part, the crus cerebri, and a posterior part, tegmentum. The tectum is lay dorsal to an oblique coronal plane which includes the aquaduct, and consist of pretectal area and the corpora quadrigemina. In transvers section, the cerebral peduncles are seen to be composed of dorsal and ventral regions separated by the substantia nigra. Tegmentum mesencephali contains red nucleus, oculomotor nucleus, thochlear nucleus, reticular nuclei, medial lemnisci, lateral lemnisci and medial longitudinal fasciculus. In tectum, the inferior colliculus and superior colliculus have main nucleus, which are continuous with the periaqueductal grey matter. The mesencephalon serves important functions in motor movement, particularly movements of the eye, and in auditory and visual processing. The mesencephalic syndrome cause tremor, spastic paresis or paralysis, opisthotonos, nystagmus and depression or coma. In addition cranial trauma, brain tumors, thiamin deficiency and inflammatory or degenerative disorders of the mesencephalon have also been associated with the midbrain syndrome
Waves on Noncommutative Spacetimes
Waves on ``commutative'' spacetimes like R^d are elements of the commutative
algebra C^0(R^d) of functions on R^d. When C^0(R^d) is deformed to a
noncommutative algebra {\cal A}_\theta (R^d) with deformation parameter \theta
({\cal A}_0 (R^d) = C^0(R^d)), waves being its elements, are no longer
complex-valued functions on R^d. Rules for their interpretation, such as
measurement of their intensity, and energy, thus need to be stated. We address
this task here. We then apply the rules to interference and diffraction for d
\leq 4 and with time-space noncommutativity. Novel phenomena are encountered.
Thus when the time of observation T is so brief that T \leq 2 \theta w, where w
is the frequency of incident waves, no interference can be observed. For larger
times, the interference pattern is deformed and depends on \frac{\theta w}{T}.
It approaches the commutative pattern only when \frac{\theta w}{T} goes to 0.
As an application, we discuss interference of star light due to cosmic strings.Comment: 19 pages, 5 figures, LaTeX, added references, corrected typo
Interacting Quantum Topologies and the Quantum Hall Effect
The algebra of observables of planar electrons subject to a constant
background magnetic field B is given by A_theta(R^2) x A_theta(R^2) the product
of two mutually commuting Moyal algebras. It describes the free Hamiltonian and
the guiding centre coordinates. We argue that A_theta(R^2) itself furnishes a
representation space for the actions of these two Moyal algebras, and suggest
physical arguments for this choice of the representation space. We give the
proper setup to couple the matter fields based on A_theta(R^2) to
electromagnetic fields which are described by the abelian commutative gauge
group G_c(U(1)), i.e. gauge fields based on A_0(R^2). This enables us to give a
manifestly gauge covariant formulation of integer quantum Hall effect (IQHE).
Thus, we can view IQHE as an elementary example of interacting quantum
topologies, where matter and gauge fields based on algebras A_theta^prime with
different theta^prime appear. Two-particle wave functions in this approach are
based on A_theta(R^2) x A_theta(R^2). We find that the full symmetry group in
IQHE, which is the semi-direct product SO(2) \ltimes G_c(U(1)) acts on this
tensor product using the twisted coproduct Delta_theta. Consequently, as we
show, many particle sectors of each Landau level have twisted statistics. As an
example, we find the twisted two particle Laughlin wave functions.Comment: 10 pages, LaTeX, Corrected typos, Published versio
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