Comments on AdS2 solutions of D=11 Supergravity

We study the supersymmetric solutions of 11-dimensional supergravity with a factor of $AdS_2$ made of M2-branes. Such solutions can provide gravity duals of superconformal quantum mechanics, or through double Wick rotation, the generic bubbling geometry of M-theory which are 1/16-BPS. We show that, when the internal manifold is compact, it should take the form of a warped U(1)-fibration over an 8-dimensional Kahler space.Comment: 11 pages, no figure, JHEP3.cl

Wiedemann-Franz violation in the vortex state of a d-wave superconductor

We show that the Wiedemann-Franz law is violated in the vortex state of a d-wave superconductor at zero temperature. We use a semiclassical approach, which includes the Doppler shift on the quasiparticles as well as the Andreev scattering from a random distribution of vortices. We also show that the vertex corrections to the electrical conductivity due to the anisotropy of impurity scattering become unimportant in the presence of a sufficiently large magnetic field.Comment: To be published in Physica C as a proceeding of M2S-HTSC Rio 200

Geometries with Killing Spinors and Supersymmetric AdS Solutions

The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in $2n+2$ dimensions, specified by a Riemannian metric, a scalar field and a closed three-form, which admit a particular kind of Killing spinor. In particular, for $n\ge 3$, we show that when the geometry in $2n+2$ dimensions is a cone we obtain a class of geometries in $2n+1$ dimensions, specified by a Riemannian metric, a scalar field and a closed two-form, which includes the seven and nine-dimensional geometries mentioned above when $n=3,4$, respectively. We also consider various ansatz for the geometries and construct infinite classes of explicit examples for all $n$.Comment: 28 page

1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry

In this paper we generalize the work of Lin, Lunin and Maldacena on the classification of 1/2-BPS M-theory solutions to a specific class of 1/4-BPS configurations. We are interested in the solutions of 11 dimensional supergravity with $SO(3)\times SO(4)$ symmetry, and it is shown that such solutions are constructed over a one-parameter familiy of 4 dimensional almost Calabi-Yau spaces. Through analytic continuations we can obtain M-theory solutions having $AdS_2\times S^3$ or $AdS_3\times S^2$ factors. It is shown that our result is equivalent to the $AdS$ solutions which have been recently reported as the near-horizon geometry of M2 or M5-branes wrapped on 2 or 4-cycles in Calabi-Yau threefolds. We also discuss the hierarchy of M-theory bubbles with different number of supersymmetries.Comment: 22 pages, JHEP3.cls; v2. revised version. showed that our results agree with previous works hep-th/0605146 and hep-th/061219

AdS(3) Solutions of IIB Supergravity from D3-branes

We consider pure D3-brane configurations of IIB string theory which lead to supersymmetric solutions containing an AdS$_3$ factor. They can provide new examples of AdS$_3$/CFT$_2$ examples on D3-branes whose worldvolume is partially compactified. When the internal 7 dimensional space is non-compact, they can be identified as supersymmetric fluctuations of higher dimensional AdS solutions and are in general dual to 1/8-BPS operators thereof. We find that supersymmetry requires the 7 dimensional space take the form of a warped U(1) fibration over a 6 dimensional Kahler manifold.Comment: 10 pages, no figure, JHEP3.cls; v3: corrected errors in the published versio

Supersymmetric AdS_3, AdS_2 and Bubble Solutions

We present new supersymmetric AdS_3 solutions of type IIB supergravity and AdS_2 solutions of D=11 supergravity. The former are dual to conformal field theories in two dimensions with N=(0,2) supersymmetry while the latter are dual to conformal quantum mechanics with two supercharges. Our construction also includes AdS_2 solutions of D=11 supergravity that have non-compact internal spaces which are dual to three-dimensional N=2 superconformal field theories coupled to point-like defects. We also present some new bubble-type solutions, corresponding to BPS states in conformal theories, that preserve four supersymmetries.Comment: v2: 33 pages, published version in JHE

Consistent supersymmetric Kaluza--Klein truncations with massive modes

We construct consistent Kaluza--Klein reductions of D=11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki--Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the Sasaki--Einstein space, and still consistent with N=2 supersymmetry. In the context of flux compactifications, the Sasaki--Einstein reductions are generalizations of type IIA SU(3)-structure reductions which include both metric and form-field flux and lead to a massive universal tensor multiplet. We carry out a similar analysis for an arbitrary weak G_2 manifold leading to an N=1 supergravity with massive fields. The straightforward extension of our results to the case of the seven-sphere would imply that there is a four-dimensional Lagrangian with N=8 supersymmetry containing both massless and massive spin two fields. We use our results to construct solutions of M-theory with non-relativistic conformal symmetry.Comment: 33 pages. v2: Added section on skew-whiffed solutions and some brief comments on holographic superconductors. v3: typos corrected, version to be published in JHE

String compactification, QCD axion and axion-photon-photon coupling

It is pointed out that there exist a few problems to be overcome toward an observable sub-eV QCD axion in superstring compactification. We give a general expression for the axion decay constant. For a large domain wall number $N_{DW}$, the axion decay constant can be substantially lowered from a generic value of a scalar singlet VEV. The Yukawa coupling structure in the recent $Z_{12-I}$ model is studied completely, including the needed nonrenormalizable terms toward realistic quark and lepton masses. In this model we find an approximate global symmetry and vacuum so that a QCD axion results but its decay constant is at the GUT scale. The axion-photon-photon coupling is calculated for a realistic vacuum satisfying the quark and lepton mass matrix conditions. It is the first time calculation of $c_{a\gamma\gamma}$ in realistic string compactifications: $c_{a\gamma\gamma}={5/3}-1.93\simeq -0.26$.Comment: 33 pages, 2 figures, JHEP format, some errors in the superpotential couplings are corrected and the following discussions are changed correspondingl

Spacetime singularity resolution by M-theory fivebranes: calibrated geometry, Anti-de Sitter solutions and special holonomy metrics

The supergravity description of various configurations of supersymmetric M-fivebranes wrapped on calibrated cycles of special holonomy manifolds is studied. The description is provided by solutions of eleven-dimensional supergravity which interpolate smoothly between a special holonomy manifold and an event horizon with Anti-de Sitter geometry. For known examples of Anti-de Sitter solutions, the associated special holonomy metric is derived. One explicit Anti-de Sitter solution of M-theory is so treated for fivebranes wrapping each of the following cycles: K\"{a}hler cycles in Calabi-Yau two-, three- and four-folds; special lagrangian cycles in three- and four-folds; associative three- and co-associative four-cycles in $G_2$ manifolds; complex lagrangian four-cycles in $Sp(2)$ manifolds; and Cayley four-cycles in $Spin(7)$ manifolds. In each case, the associated special holonomy metric is singular, and is a hyperbolic analogue of a known metric. The analogous known metrics are respectively: Eguchi-Hanson, the resolved conifold and the four-fold resolved conifold; the deformed conifold, and the Stenzel four-fold metric; the Bryant-Salamon-Gibbons-Page-Pope $G_2$ metrics on an $\mathbb{R}^4$ bundle over $S^3$, and an $\mathbb{R}^3$ bundle over $S^4$ or $\mathbb{CP}^2$; the Calabi hyper-K\"{a}hler metric on $T^*\mathbb{CP}^2$; and the Bryant-Salamon-Gibbons-Page-Pope $Spin(7)$ metric on an $\mathbb{R}^4$ bundle over $S^4$. By the AdS/CFT correspondence, a conformal field theory is associated to each of the new singular special holonomy metrics, and defines the quantum gravitational physics of the resolution of their singularities.Comment: 1+52 page

Photoplastic SU-8 probes for Near-Field Optical Applications

We propose a new attempt to solve the manufacturing problem of SNOM probes by a novel wafer-scale microfabrication process for sharp pyramidal and bright photoplastic probes. The probes are fabricated of a transparent photoplastic material (SU-8) which allows simple batch fabrication based on spin coating and subsequent near-ultraviolet exposure and development steps. SU-8 consists of the epoxy-based EPON SU-8 resin photosensitized with a triaryl sulfonium salt. The main interest for MOEMS applications is that SU-8 is transparent. These combined advantages are used here to define a sharp, transparent and high aspect ratio probe dedicated for near-field optical application