Ads(3)/CFT(2) to Ads(2)/CFT(1)

It has been suggested that the quantum generalization of the Wald entropy for an extremal black hole is the logarithm of the ground state degeneracy of a dual quantum mechanics in a fixed charge sector. We test this proposal for supersymmetric extremal BTZ black holes for which there is an independent definition of the quantum entropy as the logarithm of the degeneracy of appropriate states in the dual 1+1 dimensional superconformal field theory. We find that the two proposals agree. This analysis also suggests a possible route to deriving the OSV conjecture.Comment: LaTeX file, 14 pages; v2: references added; v3: comments and refernces added; v4: expanded discussion on the role of cut-of

On the universal hydrodynamics of strongly coupled CFTs with gravity duals

It is known that the solutions of pure classical 5D gravity with $AdS_5$ asymptotics can describe strongly coupled large N dynamics in a universal sector of 4D conformal gauge theories. We show that when the boundary metric is flat we can uniquely specify the solution by the boundary stress tensor. We also show that in the Fefferman-Graham coordinates all these solutions have an integer Taylor series expansion in the radial coordinate (i.e. no $log$ terms). Specifying an arbitrary stress tensor can lead to two types of pathologies, it can either destroy the asymptotic AdS boundary condition or it can produce naked singularities. We show that when solutions have no net angular momentum, all hydrodynamic stress tensors preserve the asymptotic AdS boundary condition, though they may produce naked singularities. We construct solutions corresponding to arbitrary hydrodynamic stress tensors in Fefferman-Graham coordinates using a derivative expansion. In contrast to Eddington-Finkelstein coordinates here the constraint equations simplify and at each order it is manifestly Lorentz covariant. The regularity analysis, becomes more elaborate, but we can show that there is a unique hydrodynamic stress tensor which gives us solutions free of naked singularities. In the process we write down explicit first order solutions in both Fefferman-Graham and Eddington-Finkelstein coordinates for hydrodynamic stress tensors with arbitrary $\eta/s$. Our solutions can describe arbitrary (slowly varying) velocity configurations. We point out some field-theoretic implications of our general results.Comment: 39 pages, two appendices added, in appendix A the proof of the power series solution has been detailed, in appendix B, we have commented on method of fixing $\eta/s$ by calculating curvature invariant

Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N=4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter--BPS black holes in N=4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over Z(N) orbifolds of higher-dimensional spheres and hyperboloids.Comment: 41 page

Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter--BPS black holes in N=4 supergravity and one--eighth BPS black holes in N=8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half--BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of SL(2,R), a result which is of possible mathematical interest.Comment: 40 page

Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets

We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.Comment: 28+16 pages, improved discussion on the boundary mode in the 4.2 and conclusion sectio

Genome Profiling of Two Strains of the Green Alga Chlamydomnas Raudensis

Chlamydomonas raudensis Ettl consists of two strains, SAG 49.72 and UWO 241. They have identical Internal Transcribed Spacer sequences and are thus considered to belong to the same species, even though they are geographically separate and physiologically and biochemically very distinct. Using the technique of random amplification of polymorphic DNA to measure the extent of genome polymorphism, the aim of this research was to estimate the similarity of the nuclear genomes of the two strains. The analysis shows that the two strains only share approximately 10% of the total number of amplicons. Surprisingly, the data also indicates, indirectly, that the genome sequences of these two strains are no more similar to each other than either is to a strain of C. reinhardtii. This research raises the intriguing question of how two strains can have identical Internal Transcribed Spacer sequences and yet possess genome sequences that are clearly divergent

A Review on AI Chip Design

In recent years, artificial intelligence (AI) technologies have been widely used in many business areas. With the attention and investment of scientific researchers and research companies around the world, artificial intelligence technologies have proven their irreplaceable value in traditional speech recognition, image recognition, search/recommendation engines, and other areas. At the same time, however, the computational effort for artificial intelligence technologies is increasing dramatically, posing a huge challenge to the computing power of hardware devices. First, in this paper, we describe the direction of AI chip technology development, including the technical shortcomings of existing AI chips. So, we present the directions of AI chip development in recent years

Neural Network Based Indexing and Recognition of Power Quality Disturbances

Power quality (PQ) analysis has become imperative for utilities as well as for consumers due to huge cost burden of poor power quality. Accurate recognition of PQ disturbances is still a challenging task, whereas methods for its indexing are not much investigated yet. This paper expounds a system, which includes generation of unique patterns called signatures of various PQ disturbances using continuous wavelet transform (CWT) and recognition of these signatures using feed-forward neural network. It is also corroborated that the size of signatures of PQ disturbances are proportional to its magnitude, so this feature of the signature is used for indexing the level of PQ disturbance in three sub-classes’ viz. high, medium, and low. Further, the effect of number of neurons used by neural network on the performance of recognition is also analyzed. Almost 100% accuracy of recognition substantiates the effectiveness of the proposed system.