BPS black holes, the Hesse potential, and the topological string

The Hesse potential is constructed for a class of four-dimensional N=2 supersymmetric effective actions with S- and T-duality by performing the relevant Legendre transform by iteration. It is a function of fields that transform under duality according to an arithmetic subgroup of the classical dualities reflecting the monodromies of the underlying string compactification. These transformations are not subject to corrections, unlike the transformations of the fields that appear in the effective action which are affected by the presence of higher-derivative couplings. The class of actions that are considered includes those of the FHSV and the STU model. We also consider heterotic N=4 supersymmetric compactifications. The Hesse potential, which is equal to the free energy function for BPS black holes, is manifestly duality invariant. Generically it can be expanded in terms of powers of the modulus that represents the inverse topological string coupling constant, $g_s$, and its complex conjugate. The terms depending holomorphically on $g_s$ are expected to correspond to the topological string partition function and this expectation is explicitly verified in two cases. Terms proportional to mixed powers of $g_s$ and $\bar g_s$ are in principle present.Comment: 28 pages, LaTeX, added comment

Nernst branes from special geometry

We construct new black brane solutions in $U(1)$ gauged ${\cal N}=2$ supergravity with a general cubic prepotential, which have entropy density $s\sim T^{1/3}$ as $T \rightarrow 0$ and thus satisfy the Nernst Law. By using the real formulation of special geometry, we are able to obtain analytical solutions in closed form as functions of two parameters, the temperature $T$ and the chemical potential $\mu$. Our solutions interpolate between hyperscaling violating Lifshitz geometries with $(z,\theta)=(0,2)$ at the horizon and $(z,\theta)=(1,-1)$ at infinity. In the zero temperature limit, where the entropy density goes to zero, we recover the extremal Nernst branes of Barisch et al, and the parameters of the near horizon geometry change to $(z,\theta)=(3,1)$.Comment: 37 pages. v2: numerical pre-factors of scalar fields q_A corrected in Section 3. No changes to conclusions. References adde

BPS dyons and Hesse flow

We revisit BPS solutions to classical N=2 low energy effective gauge theories. It is shown that the BPS equations can be solved in full generality by the introduction of a Hesse potential, a symplectic analog of the holomorphic prepotential. We explain how for non-spherically symmetric, non-mutually local solutions, the notion of attractor flow generalizes to gradient flow with respect to the Hesse potential. Furthermore we show that in general there is a non-trivial magnetic complement to this flow equation that is sourced by the momentum current in the solution.Comment: 25 pages, references adde

Gait profile score and movement analysis profile in patients with Parkinson's disease during concurrent cognitive load

Background: Gait disorders are common in individuals with Parkinson's Disease (PD) and the concurrent performance of motor and cognitive tasks can have marked effects on gait. The Gait Profile Score (GPS) and the Movement Analysis Profile (MAP) were developed in order to summarize the data of kinematics and facilitate understanding of the results of gait analysis. Objective: To investigate the effectiveness of the GPS and MAP in the quantification of changes in gait during a concurrent cognitive load while walking in adults with and without PD. Method: Fourteen patients with idiopathic PD and nine healthy subjects participated in the study. All subjects performed single and dual walking tasks. The GPS/MAP was computed from three-dimensional gait analysis data. Results: Differences were found between tasks for GPS (P<0.05) and Gait Variable Score (GVS) (pelvic rotation, knee flexion-extension and ankle dorsiflexion-plantarflexion) (P<0.05) in the PD group. An interaction between task and group was observed for GPS (P<0.01) for the right side (Cohen's d=0.99), left side (Cohen's d=0.91), and overall (Cohen's d=0.88). No interaction was observed only for hip internal-external rotation and foot internal-external progression GVS variables in the PD group. Conclusions: The results showed gait impairment during the dual task and suggest that GPS/MAP may be used to evaluate the effects of concurrent cognitive load while walking in patients with PD

Leaves, not roots or floral tissue, are the main site of rapid, external pressure-induced ABA biosynthesis in angiosperms

Rapid biosynthesis of abscisic acid (ABA) in the leaf, triggered by a decrease in cell volume, is essential for a functional stomatal response to vapour pressure deficit (VPD) in angiosperms. However, it is not known whether rapid biosynthesis of ABA is triggered in other plant tissues as well. Through the application of external pressure to flower, root and leaf tissues, we test whether a reduction in cell volume can trigger rapid increases in ABA levels across plant body in two species Solanum lycopersicum and Passiflora tarminiana. Our results show that, in contrast to rapid ABA synthesis in the leaf, flower and root tissue did not show a significant, rapid increase in ABA level in response to a drop in cell volume over a short time-frame, suggesting that fast ABA biosynthesis occurs only in leaf, not in flower or root tissues. A gene encoding the key, rate-limiting carotenoid cleavage enzyme (9`-cis-epoxycarotenoid dioxygenase, NCED) in ABA biosynthetic pathway in S. lycopersicum, NCED1, was unregulated to lesser degree in flowers and roots compared to leaves in response to applied pressure. In both species, floral tissues contained substantially lower levels of NCED substrate 9`-cis-neoxanthin than leaves, and this ABA precursor could not be detected in roots. Slow and minimal ABA biosynthesis was detected after 2 h in petals, indicating that floral tissue is capable of synthesising ABA in response to sustained water deficit. Our results indicate that rapid ABA biosynthesis predominantly occurs in the leaves, and not in other tissues

Pituitary apoplexy can mimic acute meningoencephalitis or subarachnoid haemorrhage

Pituitary apoplexy is an uncommon but life-threatening condition that is often overlooked and underdiagnosed. We report a 45-year-old man who presented to our emergency department with a sudden onset headache, acute confusion, signs of meningeal irritation and ophthalmoplegia. An initial diagnosis of acute meningoencephalitis was made, which was amended to pituitary apoplexy following thorough investigation within the emergency department

The Hesse potential, the c-map and black hole solutions

We present a new formulation of the local c-map, which makes use of the real formulation of special Kahler geometry and the associated Hesse potential. As an application we use the temporal version of the c-map to derive the black hole attractor equations from geometric properties of the scalar manifold, and we construct various stationary solutions for four-dimensional vector multiplets by lifting instanton solutions of the time-reduced theory.Comment: 76 pages. Second revised version: substantial extension. Further references added and discussion extended. Construction of axion-free non-BPS extremal solutions for a class of non-homogeneous target spaces added. Accepted for publication in JHE

Linear Sigma Models with Torsion

Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models with branes. As a non-compact example, we describe a family of metrics which correspond to deformations of the heterotic conifold by turning on H-flux. We then describe compact models which are gauge-invariant only at the quantum level. Our construction gives a generalization of symplectic reduction. The resulting spaces are non-Kahler analogues of familiar toric spaces like complex projective space. Perturbatively conformal models can be constructed by considering intersections.Comment: 40 pages, LaTeX, 1 figure; references added; a new section on supersymmetry added; quantization condition revisite