Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories

We carry out a gauge invariant analysis of certain perturbations of $D-2$-branes solutions of low energy string theories. We get generically a system of second order coupled differential equations, and show that only in very particular cases it is possible to reduce it to just one differential equation. Later, we apply it to a multi-parameter, generically singular family of constant dilaton solutions of non-critical string theories in $D$ dimensions, a generalization of that recently found in arXiv:0709.0471[hep-th]. According to arguments coming from the holographic gauge theory-gravity correspondence, and at least in some region of the parameters space, we obtain glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special emphasis in the scalar metric perturbations not considered previously in the literature in the non critical setup. We compare our numerical results to those studied previously and to lattice results, finding qualitative and in some cases, tuning properly the parameters, quantitative agreement. These results seem to show some kind of universality of the models, as well as an irrelevance of the singular character of the solutions. We also develop the analysis for the T-dual, non trivial dilaton family of solutions, showing perfect agreement between them.Comment: A new reference added

Modelling of the radiative properties of an opaque porous ceramic layer

Solid Oxide Fuel Cells (SOFCs) operate at temperatures above 1,100 K where radiation effects can be significant. Therefore, an accurate thermal model of an SOFC requires the inclusion of the contribution of thermal radiation. This implies that the thermal radiative properties of the oxide ceramics used in the design of SOFCs must be known. However, little information can be found in the literature concerning their operating temperatures. On the other hand, several types of ceramics with different chemical compositions and microstructures for designing efficient cells are now being tested. This is a situation where the use of a numerical tool making possible the prediction of the thermal radiative properties of SOFC materials, whatever their chemical composition and microstructure are, may be a decisive help. Using this method, first attempts to predict the radiative properties of a lanthanum nickelate porous layer deposited onto an yttria stabilized zirconium substrate can be reported

Stringy effects in black hole decay

We compute the low energy decay rates of near-extremal three(four) charge black holes in five(four) dimensional N=4 string theory to sub-leading order in the large charge approximation. This involves studying stringy corrections to scattering amplitudes of a scalar field off a black hole. We adapt and use recently developed techniques to compute such amplitudes as near-horizon quantities. We then compare this with the corresponding calculation in the microscopic configuration carrying the same charges as the black hole. We find perfect agreement between the microscopic and macroscopic calculations; in the cases we study, the zero energy limit of the scattering cross section is equal to four times the Wald entropy of the black hole.Comment: 32 page

On the Existence of Meta-stable Vacua in Klebanov-Strassler

We solve for the complete space of linearized deformations of the Klebanov-Strassler background consistent with the symmetries preserved by a stack of anti-D3 branes smeared on the $S^3$ of the deformed conifold. We find that the only solution whose UV physics is consistent with that of a perturbation produced by anti-D3 branes must have a singularity in the infrared, coming from NS and RR three-form field strengths whose energy density diverges. If this singularity is admissible, our solution describes the backreaction of the anti-D3 branes, and is thus likely to be dual to the conjectured metastable vacuum in the Klebanov-Strassler field theory. If this singularity is not admissible, then our analysis strongly suggests that anti-D3 branes do not give rise to metastable Klebanov-Strassler vacua, which would have dramatic consequences for some string theory constructions of de Sitter space. Key to this result is a simple, universal form for the force on a probe D3-brane in our ansatz.Comment: 35 pages, LaTeX. v2: further details provided regarding the IR singularity and the discussion modified accordingly. typos corrected, refs adde

The non-compact elliptic genus: mock or modular

We analyze various perspectives on the elliptic genus of non-compact supersymmetric coset conformal field theories with central charge larger than three. We calculate the holomorphic part of the elliptic genus via a free field description of the model, and show that it agrees with algebraic expectations. The holomorphic part of the elliptic genus is directly related to an Appell-Lerch sum and behaves anomalously under modular transformation properties. We analyze the origin of the anomaly by calculating the elliptic genus through a path integral in a coset conformal field theory. The path integral codes both the holomorphic part of the elliptic genus, and a non-holomorphic remainder that finds its origin in the continuous spectrum of the non-compact model. The remainder term can be shown to agree with a function that mathematicians introduced to parameterize the difference between mock theta functions and Jacobi forms. The holomorphic part of the elliptic genus thus has a path integral completion which renders it non-holomorphic and modular.Comment: 13 page

In-vivo high resolution imaging of optic nerve head drusen using spectral-domain Optical Coherence Tomography

<p>Abstract</p> <p>Background</p> <p>Optic nerve head drusen (ONHD) are white calcareous deposits, seen either superficially on the optic nerve head or buried within it. Diagnosis of ONHD is made by one or more ways: clinical exam, autofluorescence, ultrasound of the optic nerve, CT scan and/or visual field examination. The present study describes features of ONHD based on another diagnostic modality, the spectral-domain OCT (Spectralis).</p> <p>Methods</p> <p>This is a retrospective case series of 5 patients with bilateral ONHD with a best-corrected visual acuity of 20/20 and no other posterior segment pathology. All the patients underwent fundus photography, fundus autofluorescence, B-scan ultrasonography, Spectralis OCT and Humphrey 30-2 threshold visual fields.</p> <p>Results</p> <p>All 5 patients had surface ONHD which were autofluorescent and echodense on B-scan ultrasonography. Spectralis OCT findings in the corresponding areas include 'scattered spots with high reflectivity' casting a shadow underneath. The reflectivity can be distinctly differentiated from the blood vessels on the optic nerve. Two patients had an arcuate scotoma on the Humphrey visual fields. No correlation was found between the changes on Spectralis OCT with that of visual field.</p> <p>Conclusions</p> <p>Spectralis OCT is another useful ancillary investigation in the diagnosis of ONHD and we describe the features in the present study.</p

A slice of AdS_5 as the large N limit of Seiberg duality

A slice of AdS_5 is used to provide a 5D gravitational description of 4D strongly-coupled Seiberg dual gauge theories. An (electric) SU(N) gauge theory in the conformal window at large N is described by the 5D bulk, while its weakly coupled (magnetic) dual is confined to the IR brane. This framework can be used to construct an N = 1 MSSM on the IR brane, reminiscent of the original Randall-Sundrum model. In addition, we use our framework to study strongly-coupled scenarios of supersymmetry breaking mediated by gauge forces. This leads to a unified scenario that connects the extra-ordinary gauge mediation limit to the gaugino mediation limit in warped space.Comment: 47 Pages, axodraw4j.st

Negative discriminant states in N=4 supersymmetric string theories

Single centered BPS black hole solutions exist only when the charge carried by the black hole has positive discriminant. On the other hand the exact dyon spectrum in heterotic string theory compactified on T^6 is known to contain states with negative discriminant. We show that all of these negative discriminant states can be accounted for as two centered black holes. Thus after the contribution to the index from the two centered black holes is subtracted from the total microscopic index, the index for states with negative discriminant vanishes even for finite values of charges, in agreement with the results from the black hole side. Bound state metamorphosis -- which requires us to identify certain apparently different two centered configurations according to a specific set of rules -- plays a crucial role in this analysis. We also generalize these results to a class of CHL string theories.Comment: LaTeX file, 32 pages; v2: reference added; v3: added new section 3.

Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function

We evaluate the one loop determinant of matter multiplet fields of N=4 supergravity in the near horizon geometry of quarter BPS black holes, and use it to calculate logarithmic corrections to the entropy of these black holes using the quantum entropy function formalism. We show that even though individual fields give non-vanishing logarithmic contribution to the entropy, the net contribution from all the fields in the matter multiplet vanishes. Thus logarithmic corrections to the entropy of quarter BPS black holes, if present, must be independent of the number of matter multiplet fields in the theory. This is consistent with the microscopic results. During our analysis we also determine the complete spectrum of small fluctuations of matter multiplet fields in the near horizon geometry.Comment: LaTeX file, 52 pages; v2: minor corrections, references adde

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196