Entropy function and attractors for AdS black holes

We apply Sen's entropy formalism to the study of the near horizon geometry and the entropy of asymptotically AdS black holes in gauged supergravities. In particular, we consider non-supersymmetric electrically charged black holes with AdS_2 xS^{d-2} horizons in U(1)^4 and U(1)^3 gauged supergravities in d=4 and d=5 dimensions, respectively. We study several cases including static/rotating, BPS and non-BPS black holes in Einstein as well as in Gauss-Bonnet gravity. In all examples, the near horizon geometry and black hole entropy are derived by extremizing the entropy function and are given entirely in terms of the gauge coupling, the electric charges and the angular momentum of the black hole.Comment: 27 pages, no figures, references adde

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Verbal working memory and functional large-scale networks in schizophrenia

The aim of this study was to test whether bilinear and nonlinear effective connectivity (EC) measures of working memory fMRI data can differentiate between patients with schizophrenia (SZ) and healthy controls (HC). We applied bilinear and nonlinear Dynamic Causal Modeling (DCM) for the analysis of verbal working memory in 16 SZ and 21 HC. The connection strengths with nonlinear modulation between the dorsolateral prefrontal cortex (DLPFC) and the ventral tegmental area/substantia nigra (VTA/SN) were evaluated. We used Bayesian Model Selection at the group and family levels to compare the optimal bilinear and nonlinear models. Bayesian Model Averaging was used to assess the connection strengths with nonlinear modulation. The DCM analyses revealed that SZ and HC used different bilinear networks despite comparable behavioral performance. In addition, the connection strengths with nonlinear modulation between the DLPFC and the VTA/SN area showed differences between SZ and HC. The adoption of different functional networks in SZ and HC indicated neurobiological alterations underlying working memory performance, including different connection strengths with nonlinear modulation between the DLPFC and the VTA/SN area. These novel findings may increase our understanding of connectivity in working memory in schizophrenia

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Contributions of Riemann invariants to the Entropy of Extremal Black Holes

We use the entropy function formalism introduced by A. Sen to obtain the entropy of $AdS_{2}\times S^{d-2}$ extremal and static black holes in four and five dimensions, with higher derivative terms of a general type. Starting from a generalized Einstein--Maxwell action with nonzero cosmological constant, we examine all possible scalar invariants that can be formed from the complete set of Riemann invariants (up to order 10 in derivatives). The resulting entropies show the deviation from the well known Bekenstein--Hawking area law $S=A/4G$ for Einstein's gravity up to second order derivatives.Comment: 16 pages, revised version, comments and references added, accepted for publication in JHE

4-D gauged supergravity analysis of Type IIB vacua on K3×T2/Z2K3\times T^2/Z_2

We analyze $N=2,1,0$ vacua of type IIB string theory on $K3\times T^2/Z_2$ in presence of three-form fluxes from a four dimensional supergravity viewpoint. The quaternionic geometry of the $K3$ moduli space together with the special geometry of the NS and R-R dilatons and of the $T^2$-complex structure moduli play a crucial role in the analysis. The introduction of fluxes corresponds to a particular gauging of N=2, D=4 supergravity. Our results agree with a recent work of Tripathy and Trivedi. The present formulation shows the power of supergravity in the study of effective theories with broken supersymmetry.Comment: AMS-LaTeX, 29 page

Another Look at Price Levelling and Price Averaging in the Sydney Meat Market

Simultaneous equation techniques are used to re-examine the behaviour of monthly wholesale and retail price spreads for beef, lamb and pork in Sydney over the period 1971-1988, so as to understand the factors determining the relationships between the prices at the different market levels. Hypotheses tested relate to price levelling and price averaging, and to marketing cost and turnover effects. Using the preferred three-stage least squares estimates, price levelling is confirmed at both wholesale and retail for all meats, however contrary to earlier results there is no evidence of price averaging in any of the meats. Costs are only important determinants for beef at wholesale and lamb at retail, and only the beef and lamb wholesale spreads and the lamb retail spread are negatively influenced by turnover. A structural change test reveals significantly different behavioural responses in the 1980s compared to the 1970s, so the model is re-estimated for just the 1980s. The results generally agree with those from the longer sample, with the only change being at the retail level where costs become significant for beef as well as lamb. However the level of explanatory power for the 1980-1988 models is substantially reduced from that of the full sample models

Another Look at Price Levelling and Price Averaging in the Sydney Meat Market

Simultaneous equation techniques are used to re-examine the behaviour of monthly wholesale and retail price spreads for beef, lamb and pork in Sydney over the period 1971-1988, so as to understand the factors determining the relationships between the prices at the different market levels. Hypotheses tested relate to price levelling and price averaging, and to marketing cost and turnover effects. Using the preferred three-stage least squares estimates, price levelling is confirmed at both wholesale and retail for all meats, however contrary to earlier results there is no evidence of price averaging in any of the meats. Costs are only important determinants for beef at wholesale and lamb at retail, and only the beef and lamb wholesale spreads and the lamb retail spread are negatively influenced by turnover. A structural change test reveals significantly different behavioural responses in the 1980s compared to the 1970s, so the model is re-estimated for just the 1980s. The results generally agree with those from the longer sample, with the only change being at the retail level where costs become significant for beef as well as lamb. However the level of explanatory power for the 1980-1988 models is substantially reduced from that of the full sample models.Demand and Price Analysis,