Fuzzy Extra Dimensions: Dimensional Reduction, Dynamical Generation and Renormalizability

We examine gauge theories defined in higher dimensions where theextra dimensions form a fuzzy (finite matrix) manifold. First we reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes and then we perform a generalized \`a la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging in the later case such as (i) the appearance of non-abelian gauge theories in four dimensions starting from an abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere. We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on $M^4 \times S^2$, the scalars being interpreted as gauge fields on $S^2$. Depending on the parameters of the model the low-energy gauge group can be of the form $SU(n_1) \times SU(n_2) \times U(1)$.Comment: 18 pages, Based on invited talks presented at various conferences, Minor corrections, Acknowledgements adde

Gravity and compactified branes in matrix models

A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor \theta^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are transmitted to the 4 noncompact directions via the Poisson tensor. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it might provide a way to avoid the landscape problem in string theory.Comment: 35 pages. V2: substantially revised and improved, conclusion weakened. V3: some clarifications, published version. V4: minor correctio

The 2D Continuum Radiative Transfer Problem: Benchmark Results for Disk Configurations

We present benchmark problems and solutions for the continuum radiative transfer (RT) in a 2D disk configuration. The reliability of three Monte-Carlo and two grid-based codes is tested by comparing their results for a set of well-defined cases which differ for optical depth and viewing angle. For all the configurations, the overall shape of the resulting temperature and spectral energy distribution is well reproduced. The solutions we provide can be used for the verification of other RT codes.We also point out the advantages and disadvantages of the various numerical techniques applied to solve the RT problem.Comment: 13 pages, 10 figures, To appear in Astronomy and Astrophysic

Emergent Geometry and Gravity from Matrix Models: an Introduction

A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the brane arise as fluctuations of the bosonic resp. fermionic matrices around such a background, and couple to an effective metric interpreted in terms of gravity. Suitable tools are provided for the description of the effective geometry in the semi-classical limit. The relation to noncommutative gauge theory and the role of UV/IR mixing is explained. Several types of geometries are identified, in particular "harmonic" and "Einstein" type of solutions. The physics of the harmonic branch is discussed in some detail, emphasizing the non-standard role of vacuum energy. This may provide new approach to some of the big puzzles in this context. The IKKT model with D=10 and close relatives are singled out as promising candidates for a quantum theory of fundamental interactions including gravity.Comment: Invited topical review for Classical and Quantum Gravity. 57 pages, 5 figures. V2,V3: minor corrections and improvements. V4,V5: some improvements, refs adde

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page

A Review of Noncommutative Field Theories

We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in gravity and emergent gravity.Comment: Talk presented at the XIV Mexican School on Particles and Fields, Morelia, Mexico, November 9-11, 2010; 8 pages. V2 reference adde

'Schwinger Model' on the Fuzzy Sphere

In this paper, we construct a model of spinor fields interacting with specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this 'Schwinger model'. In constructing the theory of gauge fields interacting with spinors on fuzzy sphere, we take the approach that the Dirac operator $D_q$ on q-deformed fuzzy sphere $S_{qF}^2$ is the gauged Dirac operator on fuzzy sphere. This introduces interaction between spinors and specific one parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators $D_q$ and $D$ alone. Using the path integral method, we have calculated the $2n-$point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.Comment: Minor changes, typos corrected, 18 pages, to appear in Mod. Phys. Lett.

DART-RAY: a 3D ray-tracing radiative transfer code for calculating the propagation of light in dusty galaxies

We present DART-Ray, a new ray-tracing 3D dust radiative transfer (RT) code designed specifically to calculate radiation field energy density (RFED) distributions within dusty galaxy models with arbitrary geometries. In this paper, we introduce the basic algorithm implemented in . DART-Ray which is based on a pre-calculation of a lower limit for the RFED distribution. This pre-calculation allows us to estimate the extent of regions around the radiation sources within which these sources contribute significantly to the RFED. In this way, ray-tracing calculations can be restricted to take place only within these regions, thus substantially reducing the computational time compared to a complete ray-tracing RT calculation. Anisotropic scattering is included in the code and handled in a similar fashion. Furthermore, the code utilizes a Cartesian adaptive spatial grid and an iterative method has been implemented to optimize the angular densities of the rays originated from each emitting cell. In order to verify the accuracy of the RT calculations performed by DART-Ray, we present results of comparisons with solutions obtained using the dusty 1D RT code for a dust shell illuminated by a central point source and existing 2D RT calculations of disc galaxies with diffusely distributed stellar emission and dust opacity. Finally, we show the application of the code on a spiral galaxy model with logarithmic spiral arms in order to measure the effect of the spiral pattern on the attenuation and RFED. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society

Proteomic analysis of the cerebrospinal fluid of patients with Creutzfeldt-Jakob disease

So far, only the detection of 14-3-3 proteins in cerebrospinal fluid (CSF) has been accepted as diagnostic criterion for Creutzfeldt-Jakob disease (CJD). However, this assay cannot be used for screening because of the high rate of false-positive results, whereas patients with variant CJD are often negative for 14-3-3 proteins. The aim of this study was to compare the spot patterns of CSF by 2-dimensional polyacrylamide gel electrophoresis (2D-PAGE) to search for a CJD-specific spot pattern. We analyzed the CSF of 28 patients {[}11 CJD, 9 Alzheimer's disease ( AD), 8 nondemented controls (NDC)] employing 2D-PAGE which was optimized for minimal volumes of CSF (0.1 ml; 7-cm strips). All samples were run at least three times, gels were silver stained and analyzed by an analysis software and manually revised. We could consistently match 268 spots which were then compared between all groups. By the use of 5 spots, we were able to differentiate CJD from AD or NDC with a sensitivity of 100%. CJD could also be distinguished from both groups by using a heuristic clustering algorithm of 2 spots. We conclude that this proteomic approach can differentiate CJD from other diseases and may serve as a model for other neurodegenerative diseases. Copyright (C) 2007 S. Karger AG, Basel