BPS domain walls in N=4 supergravity and dual flows

We establish the conditions for supersymmetric domain wall solutions to N=4 gauged supergravity in five dimensions. These read as BPS first-order equations for the warp factor and the scalar fields, driven by a superpotential and supplemented by a set of constraints that we specify in detail. Then we apply our results to certain consistent truncations of IIB supergravity, thus exploring their dual field theory renormalization group flows. We find a universal flow deforming superconformal theories on D3-branes at Calabi-Yau cones. Moreover, we obtain a superpotential for the solution corresponding to the baryonic branch of the Klebanov-Strassler theory, as well as the superpotential for the flow describing D3 and wrapped D5-branes on the resolved conifold.Comment: 42 pages, 1 figure. v2: minor changes, matches published versio

A supersymmetric consistent truncation for conifold solutions

We establish a supersymmetric consistent truncation of type IIB supergravity on the T^{1,1} coset space, based on extending the Papadopoulos-Tseytlin ansatz to the full set of SU(2)xSU(2) invariant Kaluza-Klein modes. The five-dimensional model is a gauged N=4 supergravity with three vector multiplets, which incorporates various conifold solutions and is suitable for the study of their dynamics. By analysing the scalar potential we find a family of new non-supersymmetric AdS_5 extrema interpolating between a solution obtained long ago by Romans and a solution employing an Einstein metric on T^{1,1} different from the standard one. Finally, we discuss some simple consistent subtruncations preserving N=2 supersymmetry. One of them still contains the Klebanov-Strassler solution, and is compatible with the inclusion of smeared D7-branes.Comment: 34 pages, 1 figure; v2: minor changes, references added, appendix C revised; v3: journal versio

Mobility improvement of heavy tracked vehicles: The "pan" tank experience

This paper shows that the sinkage of the tracked vehicle is the most important parameter in its mobility. Power and fuel consumption follow cubic power law with sinkage. So the usual strategy to increase power is not the more convenient way to improve vehicle off road performance. The Ground Pressure (GP) is the critical parameter. Power requirement goes with the cubic power of sinkage. GP above 0.9 daN/cm2 should be avoided at all costs. The best way to obtain this result on an existing design is to increase track length. However it is easier to work on track width. The easiest modification is to add "Duckbill extensions" in the outer part of the shoe. This system was used on the Sherman Tank when additional armor was added. With modern technology it is perfectly possible to perform experimental tests with new shoes. This can be done by manufacturing prototypes of high stress nitrided steel shoes, usually with 300M high strength steel. Comparative fuel consumption is a good index of vehicle performance. Also wheel diameter and width can be increased to improve off-road performance. Specialized tracks for different terrains should also be designed. The gravity center should be kept slightly rearward. This attitude should not be excessive to keep the pressure value more even possible along the track. In any case the vehicle naturally assumes the backward inclination due to terrain compression. Another important improvement is the addition of computer controlled directional control to improve the accuracy of trajectories. This is particularly important for tracked vehicles where turning involves extremely high energy consumption

Constructing Lifshitz solutions from AdS

Under general assumptions, we show that a gravitational theory in d+1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z=2. Working in a d=4, N=2 supergravity setup, we prove that if the AdS background is N=2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 x S1 x T(1,1) solution of type IIB.Comment: 29 pages, no figures; v2 minor corrections, a reference adde

Consistent reduction of charged D3-D7 systems

We provide a consistent reduction to five dimensions of the system of D3-branes at Calabi-Yau singularities coupled to D7-branes with world-volume gauge flux. The D3-branes source the dual to would-be conformal quiver theories. The D7-branes, which are homogeneously distributed in their transverse directions, are dual to massless matter in the fundamental representation at finite (baryon) density. We provide the five-dimensional action and equations of motion, and discuss a few sub-truncations. The reduction can be used in the study of transport properties and stability of D3-D7 charged systems.Comment: 23 pages. v2: references added and minor change

de Sitter Supersymmetry Revisited

We present the basic $\mathcal{N} =1$ superconformal field theories in four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills theory and the chiral multiplet theory with gauge interactions or cubic superpotential. These theories have eight supercharges and are invariant under the full $SO(4,2)$ group of conformal symmetries, which includes the de Sitter isometry group $SO(4,1)$ as a subgroup. The theories are ghost-free and the anti-commutator $\sum_\alpha\{Q_\alpha, Q^{\alpha\dagger}\}$ is positive. SUSY Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum state is invariant under superconformal transformations, despite the fact that de Sitter space has non-zero Hawking temperature. The $\mathcal{N}=1$ theories are classically invariant under the $SU(2,2|1)$ superconformal group, but this symmetry is broken by radiative corrections. However, no such difficulty is expected in the $\mathcal{N}=4$ theory, which is presented in appendix B.Comment: 21 pages, 2 figure

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo

Heterotic Flux Attractors

We find attractor equations describing moduli stabilization for heterotic compactifications with generic SU(3)-structure. Complex structure and K\"ahler moduli are treated on equal footing by using SU(3)xSU(3)-structure at intermediate steps. All independent vacuum data, including VEVs of the stabilized moduli, is encoded in a pair of generating functions that depend on fluxes alone. We work out an explicit example that illustrates our methods.Comment: 37 pages, references and clarifications adde

Propargyl carbamate-functionalized Cu(II)-metal organic framework after reaction with chloroauric acid: An x-ray photoelectron spectroscopy data record

A copper-containing metal organic framework was prepared using the new organic linker 5-(2-{[(prop-2-yn-1-yloxy)carbonyl]-amino} ethoxy)isophthalic acid [1,3-H2YBDC (where Y = alkYne and BDC = Benzene DiCarboxylate)] and functionalized with gold particles by reaction with HAuCl4 under thermal treatment in methanol. The resulting system was investigated by complementary techniques to obtain information on its structure and morphology. In the present work, x-ray photoelectron spectroscopy (XPS) was employed to analyze the chemical composition of a representative specimen. Besides wide scan spectra, data obtained by the analysis of the C 1s, O 1s, N 1s, Cu 2p, and Au 4f signals are presented and critically discussed. The results highlight the reduction of Au(III) to mostly Au(I) species. Overall, the data presented herein may act as useful guidelines for the eventual tailoring of material properties and their possible implementation toward functional applications in heterogeneous catalysis

The critical dimension for a 4th order problem with singular nonlinearity

We study the regularity of the extremal solution of the semilinear biharmonic equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under Dirichlet boundary conditions $u=\partial_\nu u=0$ on $\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the identification of a "pull-in voltage" \la^*>0 such that a stable classical solution u_\la with 0 exists for \la\in (0,\la^*), while there is none of any kind when \la>\la^*. Our main result asserts that the extremal solution $u_{\lambda^*}$ is regular $(\sup_B u_{\lambda^*} <1)$ provided $N \le 8$ while $u_{\lambda^*}$ is singular ($\sup_B u_{\lambda^*} =1$) for $N \ge 9$, in which case $1-C_0|x|^{4/3}\leq u_{\lambda^*} (x) \leq 1-|x|^{4/3}$ on the unit ball, where $C_0:= (\frac{\lambda^*}{\overline{\lambda}})^{1/3}$ and $\bar{\lambda}:= {8/9} (N-{2/3}) (N- {8/3})$.Comment: 19 pages. This paper completes and replaces a paper (with a similar title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this author's papers can be downloaded at this http://www.birs.ca/~nassif