Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter (AdS) gravity action in four dimensions recovers the standard regularization given by holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as $T_{j}^{i}=\pm (\ell ^{2}/8\pi G)C_{j}^{i}$, which has been observed in recent literature in solitonic solutions and hydrodynamic models. A general procedure to generate the counterterm series for AdS gravity in any even dimension from the corresponding Euler term is also briefly discussed.Comment: 13 pages, no figures; enlarged discussion on self-duality condition for AAdS spacetimes, references added, final version for PR

Thermodynamics of Einstein-Born-Infeld black holes with negative cosmological constant

We study the thermodynamics associated to topological black hole solutions of AdS gravity coupled to nonlinear electrodynamics (Born-Infeld) in any dimension, using a background-independent regularization prescription for the Euclidean action given by boundary terms which explicitly depend on the extrinsic curvature (Kounterterms series). A finite action principle leads to the correct definition of thermodynamic variables as Noether charges, which satisfy a Smarr-like relation. In particular, for the odd-dimensional case, a consistent thermodynamic description is achieved if the internal energy of the system includes the vacuum energy for AdS spacetime.Comment: 29 pages, no figures; additional comments on extreme black hole case, a few references added; final version for PR

Couplings between Chern-Simons gravities and 2p-branes

The interaction between Chern-Simons (CS) theories and localized external sources (2p-branes) is analyzed. This interaction generalizes the minimal coupling between a point charge (0-brane) and a gauge connection. The external currents that define the 2p-branes are covariantly constant (D-2p-1)-forms coupled to (2p-1) CS forms. The general expression for the sources --charged with respect to the corresponding gauge algebra-- is presented, focusing on two special cases: 0-branes and (D-3)-branes. In any dimension, 0-branes are constructed as topological defects produced by a surface deficit of (D-2)-sphere in AdS space, and they are not constant curvature spaces for D>3. They correspond to dimensionally continued black holes with negative mass. On the other hand, in the case of CS (super) gravities, the (D-3)-branes are naked conical singularities (topological defects) obtained by identification of points with a Killing vector. In 2+1 dimensions, extremal spinning branes of this type are BPS states. Stable (D-3)-branes are shown to exist also in higher dimensions, as well. Classical field equations are also discussed and in the presence of sources there is a large number of inequivalent and disconnected sectors in solution space.Comment: 29 pages, no figures; version accepted in PRD; extended introduction and several references added; some sections have been reorganized and several minor corrections mad

Stable p-branes in Chern-Simons AdS supergravities

We construct static codimension-two branes in any odd dimension D, with negative cosmological constant, and show that they are exact solutions of Chern-Simons (super)gravity theory for (super)AdS coupled to external sources. The stability of these solutions is analyzed by counting the number of preserved supersymmetries. It is shown that static massive (D-3)-branes are unstable unless some suitable gauge fields are added and the brane is extremal. In particular, in three dimensions, a 0-brane is recognized as the negative mass counterpart of the BTZ black hole. For these 0-branes, we write explicitly electromagnetically charged BPS states with various number of preserved supersymmetries within the OSp(p|2) x OSp(q|2) supergroups. In five dimensions, we prove that stable 2-branes with electromagnetic charge always exist for the generic supergroup SU(2,2|N), where N is different than 4. For the special case N=4, in which the CS supergravity requires the addition of a nontrivial gauge field configuration in order to preserve maximal number of degrees of freedom, we show for two different static 2-branes that they are BPS states (one of which is the ground state), and from the corresponding algebra of charges we show that the energy is bounded from below. In higher dimensions, our results admit a straightforward generalization, although there are presumably more solutions corresponding to different intersections of the elementary objects.Comment: 43 pages, revtex4.cls; v2: slight amendments and references added to match published versio

Geometry and stability of spinning branes in AdS gravity

The geometry of spinning codimension-two branes in AdS spacetime is analyzed in three and higher dimensions. The construction of non-extremal solutions is based on identifications in the covering of AdS space by isometries that have fixed points. The discussion focuses on the cases where the parameters of spinning states can be related to the velocity of a boosted static codimension-two brane. The resulting configuration describes a single spinning brane, or a set of intersecting branes, each one produced by an independent identification. The nature of the singularity is also examined, establishing that the AdS curvature acquires one in the form of a Dirac delta distribution. The stability of the branes is studied in the framework of Chern-Simons AdS supergravity. A class of branes, characterized by one free parameter, are shown to be stable when the BPS conditions are satisfied. In 3D, these stable branes are extremal, while in higher dimensions, the BPS branes are not the extremal ones.Comment: 40 pages, 6 figure

Social Cognition in Patients With Cerebellar Neurodegenerative Disorders

ObjectiveCerebellar neurodegenerative disorders (CDs) are a heterogeneous group of disorders. It is known that the cerebellum plays a role not only in motor, but also in cognitive and social cognitive functions. The aim of this study was to investigate social cognition in patients with different CDs.Materials and MethodsSocial cognition was examined in 34 patients, 12 with spinocerebellar ataxia type 1 (SCA1), 6 with spinocerebellar ataxia type 2 (SCA2), and 16 with idiopathic late onset cerebellar ataxia (ILOCA). All patients were clinically evaluated using the Scale for the Rating and Assessment of Ataxia. In addition, 34 age, sex, and education-matched healthy control (HC) subjects were similarly analyzed. Social cognition was studied using two tests: the Faux Pas Recognition Test and the Reading the Mind in the Eyes Test (RMET). An appropriate array of neuropsychological tests was used to assess the global cognitive status as well as the frontal functions and mood.ResultsCD patients achieved significantly worse results on both tests of social cognition compared to the HCs. The SCA1 + 2 group achieved the poorest results on the Faux Pas Recognition Test and exhibited poor performance on all cognitive tests, but was only significantly worse compared to the ILOCA group on the Free and Cued Selective Reminding Test (FCSRT) – recognition. The patients in the SCA1 + 2 and ILOCA groups obtained similar scores on RMET. In the SCA1 + 2 group the findings significantly correlated with clinical parameters of disease severity and duration and executive functions (EFs), and with mood and executive functions in the ILOCA group. In the SCA group EFs appeared as the only significant predictor of RMET achievement. The Boston Naming Test (BTN) was a significant predictor of the CD patients’ achievement on RMET, while the BTN, the Trail Making Test Part A and FCSRT – Delayed free recall predicted their performance on the Faux Pas Recognition Test.ConclusionPatients with CD have social cognitive impairments as demonstrated by the Faux Pas Test and the RMET test results. The SCA1 and 2 patients exhibited a more pronounced impairment compared with the ILOCA patients. The independent cognitive predictors of social cognition impairment were EFs and language

Microstructure and toughness of CuNiMo austempered ductile iron

The effect of austempering on the microstructure and toughness of nodular cast iron (designated as CuNiMoSG) alloyed with molybdenum, copper, nickel, and manganese has been studied. Light microscopy (LM), scanning electron microscopy (SEM), and X-ray diffraction technique were performed for microstructural characterization, whereas impact energy test was applied for toughness measurement. Specimens were austenitised at 860 degreesC, then austempered for various times at 320 and 400 degreesC, followed by ice-water quenching. Austempering at 320 degreesC produces a microstructure consisting of a mixture of acicular bainitic ferrite and the stable carbon-enriched austenite. In this microstructure epsilon-carbides are also identified after austempering up to 5 h. Fracture mode is changed from ductile to brittle with the prolonged time of austempering at 320 degreesC. The highest impact energy (115 kJ) corresponds not only to ductile fracture, but also to the maximum value of the volume fraction of retained austenite. Only martensitic structure was observed during austempering at 400 degreesC, inducing brittle fracture and significantly low-impact energy (10-12 kJ)

Chern-Simons action and the Carrollian Cotton tensors

Abstract In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to Carrollian diffeomorphisms in a suitable frame, one discloses four sets of Cotton Carrollian relatives, which are conformal and obey Carrollian conservation equations. Each set of Carrollian Cotton tensors is alternatively obtained as the variation of a distinct Carroll-Chern-Simons action with respect to the degenerate metric and the clock form of a strong Carroll structure. The four Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original Chern-Simons ascendant. They inherit its anomalous behaviour under diffeomorphisms and Weyl transformations. The extremums of these Carrollian actions are commented and illustrated