Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry

We use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of certain supergravity theories in $d=4$. In minimal AdS supergravity, the boundary conditions such that the supercharges exist as Hamiltonian generators of supersymmetry transformations are unique within the usual framework in which the boundary metric is fixed. In extended ${\mathcal N}=4$ AdS supergravity, or more generally in the presence of chiral matter superfields, we find that there exist many boundary conditions preserving ${\mathcal N}=1$ supersymmetry for which corresponding generators exist. These choices are shown to correspond to a choice of certain arbitrary boundary ``superpotentials,'' for suitably defined ``boundary superfields.'' We also derive corresponding formulae for the conserved bosonic charges, such as energy, in those theories, and we argue that energy is always positive, for any supersymmetry-preserving boundary conditions. We finally comment on the relevance and interpretation of our results within the AdS-CFT correspondence.Comment: 45 pages, Latex, no figures, v2: extended discussion of positive energy theorem and explicit form of fermionic generators, references adde

All Vacuum Near-Horizon Geometries in DD-dimensions with (D−3)(D-3) Commuting Rotational Symmetries

We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in $D=4,5$. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology $S^2 \times T^{D-4}$, or $S^3 \times T^{D-5}$, or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as $(D-2)(D-3)/2$ continuous parameters. Not all of our metrics in $D \ge 6$ seem to arise as the near horizon limits of known black hole solutions.Comment: 22 pages, Latex, no figures, title changed, references added, discussion of the parameters specifying solutions corrected, amended to match published versio

Initial Conditions for Vector Inflation

Recently, a model of inflation using non-minimally coupled massive vector fields has been proposed. For a particular choice of non-minimal coupling parameter and for a flat FRW model, the model is reduced to the model of chaotic inflation with massive scalar field. We study the effect of non-zero curvature of the universe on the onset of vector inflation. We find that in a curved universe the dynamics of vector inflation can be different from chaotic inflation, and the fraction of the initial conditions leading to inflationary solutions is reduced compared with the chaotic inflation case.Comment: 12 pages, 5 figures, version to be published in JCA

Methods for reducing heat losses from flat plate solar collectors: Phase III. Final report, May 1, 1977-January 31, 1979

The present study extends earlier studies by examining the effect of the emissivities of both the absorber plate and the glass cover on the honeycomb's ability to suppress free convection, and on the radiative and conductive heat transfer which takes place across the honeycomb in the absence of free convection. By means of heat transfer measurements on ten Mylar honeycombs, this study has shown that the effect of the above emissivities on the suppression of convection by the honeycomb is slight, and can probably be ignored. On the other hand, the measurements also showed that the effect of these emissivities on the non-convective heat transfer is substantial, but not nearly so large as would have been predicted by existing theories. To explain this latter result theories were developed which take into account the important coupling (ignored by previous theories) between the conductive and radiative modes of heat transfer. These new theories predict the measured heat transfer rates to with about +-15%, depending on the emissivities. The results of this study have direct application to evaluating solar collectors which combine a selective surface with a honeycomb

Flow visualization of natural convection in a tall, air-filled vertical cavity

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.ijheatmasstransfer.2005.06.045 © 2006. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Natural convection of air in a tall vertical cavity was studied using a smoke patterns and interferometry. Experiments covered Rayleigh numbers of 4850 < Ra < 54,800 and aspect ratio A ≈ 40. Secondary cells were noted at Ra as low as 6228. The flow was stable at Ra < 104. As Ra exceeded 104 the flow became irregular, the core flow became increasingly unsteady and 3-D motion became evident. Interferometry showed that most of the temperature drop exists in boundary layers near the walls. The core is well mixed and of relatively uniform temperature with little or no vertical stratification.Natural Sciences and Engineering Research Council of Canad

The gravity duals of SO/USp superconformal quivers

We study the gravity duals of SO/USp superconformal quiver gauge theories realized by M5-branes wrapping on a Riemann surface ("G-curve") together with a Z_2-quotient. When the G-curve has no punctures, the gravity solutions are classified by the genus g of the G-curve and the torsion part of the four-form flux G_4. We also find that there is an interesting relation between anomaly contributions from two mysterious theories: T_{SO(2N)} theory with SO(2N)^3 flavor symmetry and \tilde{T}_{SO(2N)} theory with SO(2N) x USp(2N-2)^2 flavor symmetry. The dual gravity solutions for various SO/USp-type tails are also studied.Comment: 27 pages, 13 figures; v2 minor corrections, typos corrected, Figure 13 replaced, references adde

Topology of supersymmetric N=1, D=4 supergravity horizons

All supersymmetric N=1, D=4 supergravity horizons have toroidal or spherical topology, irrespective of whether the black hole preserves any supersymmetry.Comment: 17 pages, latex. Alterations to introduction and section 3.

On the nonexistence of a vacuum black lens

We demonstrate that five-dimensional, asymptotically flat, stationary and biaxisymmetric, vacuum black holes with lens space $L(n, 1)$ topology, possessing the simplest rod structure, do not exist. In particular, we show that the general solution on the axes and horizon, which we recently constructed by exploiting the integrability of this system, must suffer from a conical singularity on the inner axis component. We give a proof of this for two distinct singly spinning configurations and numerical evidence for the generic doubly spinning solution.Comment: v2: minor changes, published version; 23 pages, 3 figure

On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation

Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.Comment: 43 page

Wearable Haptic Devices for Gait Re-education by Rhythmic Haptic Cueing

This research explores the development and evaluation of wearable haptic devices for gait sensing and rhythmic haptic cueing in the context of gait re-education for people with neurological and neurodegenerative conditions. Many people with long-term neurological and neurodegenerative conditions such as Stroke, Brain Injury, Multiple Sclerosis or Parkinson’s disease suffer from impaired walking gait pattern. Gait improvement can lead to better fluidity in walking, improved health outcomes, greater independence, and enhanced quality of life. Existing lab-based studies with wearable devices have shown that rhythmic haptic cueing can cause immediate improvements to gait features such as temporal symmetry, stride length, and walking speed. However, current wearable systems are unsuitable for self-managed use for in-the-wild applications with people having such conditions. This work aims to investigate the research question of how wearable haptic devices can help in long-term gait re-education using rhythmic haptic cueing. A longitudinal pilot study has been conducted with a brain trauma survivor, providing rhythmic haptic cueing using a wearable haptic device as a therapeutic intervention for a two-week period. Preliminary results comparing pre and post-intervention gait measurements have shown improvements in walking speed, temporal asymmetry, and stride length. The pilot study has raised an array of issues that require further study. This work aims to develop and evaluate prototype systems through an iterative design process to make possible the self-managed use of such devices in-the-wild. These systems will directly provide therapeutic intervention for gait re-education, offer enhanced information for therapists, remotely monitor dosage adherence and inform treatment and prognoses over the long-term. This research will evaluate the use of technology from the perspective of multiple stakeholders, including clinicians, carers and patients. This work has the potential to impact clinical practice nationwide and worldwide in neuro-physiotherapy