Fivebranes Wrapped on SLAG Three-Cycles and Related Geometry

We construct ten-dimensional supergravity solutions corresponding to the near horizon limit of IIB fivebranes wrapping special Lagrangian three-cycles of constant curvature. The case of branes wrapping a three-sphere provides a gravity dual of pure N=2 super-Yang-Mills theory in D=3. The non-trivial part of the solutions are seven manifolds that admit two G_2 structures each of which is covariantly constant with respect to a different connection with torsion. We derive a formula for the generalised calibration for this general class of solutions. We discuss analogous aspects of the geometry that arises when fivebranes wrap other supersymmetric cycles which lead to Spin(7) and SU(N) structures. In some cases there are two covariantly constant structures and in others one.Comment: v2: 26 pages, 3 figures, 1 table. Section 7 slightly expanded, references adde

Probing Non-Toric Geometry with Rotating Membranes

Recently Martelli and Sparks presented the first non-toric AdS_4/CFT_3 duality relation between M-theory on AdS_4 x V_{5,2}/Z_k and a class of three-dimensional N=2 quiver Chern-Simons-matter theories. V_{5,2} is a seven-dimensional homogeneneous Sasaki-Einstein manifold with isometry group SO(5)xU(1)_R, which is in general broken to SU(2)xU(1)xU(1)_R by the orbifold projection if k>1. The dual field theory is described by the A_1 quiver, U(N)_k x U(N)_{-k} gauge group, four bifundamentals, two adjoint chiral multiplets interacting via a cubic superpotential. We explore this proposal by studying various classical membrane solutions moving in V_{5,2}. Rotating membrane solutions of folded, wrapped, spike, and giant magnon types are presented with their dispersion relations. We also discuss their dual operators in the Chern-Simons-matter theory.Comment: 20 pages, 1 figure

M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds

Seven-dimensional inhomogeneous Sasaki-Einstein manifolds $Y^{p,k}(KE_4)$ present a challenging example of AdS/CFT correspondence. At present, their field theory duals for $KE_4=\mathbb{CP}^2$ base are proposed only within a restricted range $3p/2\le k \le 2p$ as ${\cal N}=2$ quiver Chern-Simons-matter theories with $SU(N)\times SU(N)\times SU(N)$ gauge group, nine bifundamental chiral multiplets interacting through a cubic superpotential. To further elucidate this correspondence, we use particle approximation both at classical and quantum level. We setup a concrete AdS/CFT mapping of conserved quantities using geodesic motions, and turn to solutions of scalar Laplace equation in $Y^{p,k}$. The eigenmodes also provide an interesting subset of Kaluza-Klein spectrum for $D=11$ supergravity in ${\rm AdS}_4\times Y^{p,k}$, and are dual to protected operators written in terms of matter multiplets in the dual conformal field theory.Comment: v2 refs added. 19 pages 1 figur

Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields

The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-$N$ limit, at least for vector-like models. The validity of chiral-like models is not established yet, due to technical problems in both analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested that the counting of chiral operators can be used to find the eigenvalue distribution of quiver matrix models. In this paper we apply this method to some vector-like or chiral-like quiver theories, including the triangular quivers with generic Chern-Simons levels which are dual to in-homogeneous Sasaki-Einstein manifolds $Y^{p,k}(\mathbb{CP}^2)$. The result is consistent with AdS/CFT and the volume formula. We discuss the implication of our analysis.Comment: 23 pages; v2. revised version; v3. corrected typos and clarified argument

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

Semiclassical strings in marginally deformed toric AdS/CFT

We study string solutions in the beta-deformed Sasaki-Einstein gauge/gravity dualities. We find that the BPS point-like strings move in the submanifolds where the two U(1) circles shrink to zero size. In the corresponding T^3 fibration description, the strings live on the edges of the polyhedron, where the T^3 fibration degenerates to T^1. Moreover, we find that for each deformed Sasaki-Einstein manifold the BPS string solutions exist only for particular values of the deformation parameter. Our results imply that in the dual field theory the corresponding BPS operators exist only for these particular values of the deformation parameter we find. We also examine the non-BPS strings, derive their dispersion relations and compare them with the undeformed ones. Finally, we comment on the range of the validity of our solutions and their dependence on the deformation parameter.Comment: 29 pages, 9 figure

Wheeler-DeWitt Equation in AdS/CFT Correspondence

We discuss a quantum extension of the holographic RG flow equation obtained previously from the classical Hamiltonian constraint in the bulk AdS supergravity. The Wheeler-DeWitt equation is proposed to generate the extended RG flow and to produce 1/N subleading corrections systematically. Our formulation in five dimensions is applied to the derivation of the Weyl anomaly of boundary N=4 SU(N) super-Yang-Mills theory beyond the large N limit. It is shown that subleading 1/N^2 corrections arising from fields in AdS_5 supergravity agree with those obtained recently by Mansfield et al. using their Schroedinger equation, thereby guaranteeing to reproduce the exact form of the boundary Weyl anomaly after summing up all of the KK modes.Comment: 7 pages, LaTex, references adde

The Author Response: EML4-ALK Fusion Gene in Korean Non-Small Cell Lung Cancer

I would like to thank the interest and comments on our paper entitled “EML4-ALK fusion gene in Korean non-small cell lung cancer ” (1). In this study, we examined EML4-ALK fusion variants in Korean non-small cell lung cancers (NSCLCs) via reversetranscriptase-polymerase chain reaction (RT-PCR) using primers designed to detect EML4-ALK fusion variants (variants 1, 2, 3a, 3b, 4, 5a, 5b, 6, and 7) that have been previously identified (2, 3). Our study demonstrated the spectrum and frequency of EML4-ALK fusion variants in Korean NSCLCs, which were different from those in other ethnic populations. I agree with the comment that the RT-PCR technology for identification of ALK fusion variants has several limitations. As pointed out in this comment, there are multiple EML4-ALK fusion variants and non-EML4 fusion partners, such as KIF5B, and KLC1 (2-5); therefore, any PCR-based strategy must incorporat

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

On a class of 4D Kahler bases and AdS_5 supersymmetric Black Holes

We construct a class of toric Kahler manifolds, M_4, of real dimension four, a subset of which corresponds to the Kahler bases of all known 5D asymptotically AdS_5 supersymmetric black-holes. In a certain limit, these Kahler spaces take the form of cones over Sasaki spaces, which, in turn, are fibrations over toric manifolds of real dimension two. The metric on M_4 is completely determined by a single function H(x), which is the conformal factor of the two dimensional space. We study the solutions of minimal five dimensional gauged supergravity having this class of Kahler spaces as base and show that in order to generate a five dimensional solution H(x) must obey a simple sixth order differential equation. We discuss the solutions in detail, which include all known asymptotically AdS_5 black holes as well as other spacetimes with non-compact horizons. Moreover we find an infinite number of supersymmetric deformations of these spacetimes with less spatial isometries than the base space. These deformations vanish at the horizon, but become relevant asymptotically.Comment: 34 pages, 3 figures. v2: formula (8.35) and other minor typos corrected; references added; accepted for publication in JHE