34 research outputs found
The Star Product on the Fuzzy Supersphere
The fuzzy supersphere is a finite-dimensional matrix
approximation to the supersphere incorporating supersymmetry
exactly. Here the star-product of functions on is obtained by
utilizing the OSp(2,1) coherent states. We check its graded commutative limit
to and extend it to fuzzy versions of sections of bundles using the
methods of [1]. A brief discussion of the geometric structure of our
star-product completes our work.Comment: 21 pages, LaTeX, new material added, minor errors correcte
Chirality and Dirac Operator on Noncommutative Sphere
We give a derivation of the Dirac operator on the noncommutative -sphere
within the framework of the bosonic fuzzy sphere and define Connes' triple. It
turns out that there are two different types of spectra of the Dirac operator
and correspondingly there are two classes of quantized algebras. As a result we
obtain a new restriction on the Planck constant in Berezin's quantization. The
map to the local frame in noncommutative geometry is also discussed.Comment: 24 pages, latex, no figure
Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
We generalise the construction of fuzzy CP^N in a manner that allows us to
access all noncommutative equivariant complex vector bundles over this space.
We give a simplified construction of polarization tensors on S^2 that
generalizes to complex projective space, identify Laplacians and natural
noncommutative covariant derivative operators that map between the modules that
describe noncommuative sections. In the process we find a natural
generalization of the Schwinger-Jordan construction to su(n) and identify
composite oscillators that obey a Heisenberg algebra on an appropriate Fock
space.Comment: 34 pages, v2 contains minor corrections to the published versio
Scalar Field Theory on Fuzzy S^4
Scalar fields are studied on fuzzy and a solution is found for the
elimination of the unwanted degrees of freedom that occur in the model. The
resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4
in the fuzzy context.Comment: 16 pages, LaTe
Metric Properties of the Fuzzy Sphere
The fuzzy sphere, as a quantum metric space, carries a sequence of metrics
which we describe in detail. We show that the Bloch coherent states, with these
spectral distances, form a sequence of metric spaces that converge to the round
sphere in the high-spin limit.Comment: Slightly shortened version, no major changes, two new references,
version to appear on Letters in Mathematical Physic
The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
We analyse the fluctuations of the ground-state/funnel solutions proposed to
describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter
ABJM theory of multiple membranes. We show that in the large N limit the
fluctuations approach the space of functions on the 2-sphere rather than the
naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in
the context of Matrix Theories, which uses bifundamental instead of adjoint
scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory
on R^{2,1} x S^2 is recovered at large N, which is consistent with a single
D4-brane interpretation in Type IIA string theory. This is as expected at large
k, where the semiclassical analysis is valid. Several aspects of the
fluctuation analysis, the ground-state/funnel solutions and the
mass-deformed/pure ABJM equations can be understood in terms of a discrete
noncommutative realisation of the Hopf fibration. We discuss the implications
for the possibility of finding an M2-brane worldvolume derivation of the
classical S^3 geometry of the M2-M5 system. Using a rewriting of the equations
of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare
this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show
them to be different.Comment: 60 pages, Latex; v2: references added; v3: typos corrected and
references adde
Young and Intermediate-age Distance Indicators
Distance measurements beyond geometrical and semi-geometrical methods, rely
mainly on standard candles. As the name suggests, these objects have known
luminosities by virtue of their intrinsic proprieties and play a major role in
our understanding of modern cosmology. The main caveats associated with
standard candles are their absolute calibration, contamination of the sample
from other sources and systematic uncertainties. The absolute calibration
mainly depends on their chemical composition and age. To understand the impact
of these effects on the distance scale, it is essential to develop methods
based on different sample of standard candles. Here we review the fundamental
properties of young and intermediate-age distance indicators such as Cepheids,
Mira variables and Red Clump stars and the recent developments in their
application as distance indicators.Comment: Review article, 63 pages (28 figures), Accepted for publication in
Space Science Reviews (Chapter 3 of a special collection resulting from the
May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space
Age
Physical Processes in Star Formation
© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00693-8.Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms.Peer reviewedFinal Accepted Versio