Inverting geometric transitions: explicit Calabi-Yau metrics for the Maldacena-Nunez solutions

Explicit Calabi-Yau metrics are derived that are argued to map to the Maldacena-Nu\~{n}ez AdS solutions of M-theory and IIB under geometric transitions. In each case the metrics are singular where a H^2 K\"{a}hler two-cycle degenerates but are otherwise smooth. They are derived as the most general Calabi-Yau solutions of an ansatz for the supergravity description of branes wrapped on K\"{a}hler two-cycles. The ansatz is inspired by re-writing the AdS solutions, and the structure defined by half their Killing spinors, in this form. The world-volume theories of fractional branes wrapped at the singularities of these metrics are proposed as the duals of the AdS solutions. The existence of supergravity solutions interpolating between the $AdS$ and Calabi-Yau metrics is conjectured and their boundary conditions briefly discussed.Comment: 1+17 pages, LaTeX; v2, typos corrected; v3, typos corrected, final versio

Dynamics of Probe Brane in the Background of Intersecting Fivebranes

This paper is devoted to the study of the dynamics of the Dp-branes, F-strings and M-branes in the background of the system of two stacks of fivebranes in type IIA, IIB and M theory that intersect on the line.Comment: 17.pages, reference adde

Supersymmetric AdS_3 solutions of type IIB supergravity

For every positively curved Kahler-Einstein manifold in four dimensions we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS_3 with a compact seven-dimensional manifold and have non-vanishing five-form flux. Via the AdS/CFT correspondence, the solutions are dual to two-dimensional conformal field theories with (2,0) supersymmetry. The corresponding central charges are rational numbers.Comment: Dedicated to Rafael Sorkin in celebration of his 60th birthday; 5 pages, latex. v2, typos corrected, to appear in PR

Superconformal field theories from crystal lattices

We propose a brane configuration for the (2+1)d, $\mathcal{N}=2$ superconformal theories (CFT$_3$) arising from M2-branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M-theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT$_4$. The fundamental fields of the CFT$_3$ are M2-brane discs localized around the intersections, and the super-potential terms are identified with the atoms of the crystal. The model correctly reproduces the complete BPS spectrum of mesons and baryons.Comment: 4 pages, 4 figures, revtex; v2. references added, minor correction

The Geometry of D=11 Null Killing Spinors

We determine the necessary and sufficient conditions on the metric and the four-form for the most general bosonic supersymmetric configurations of D=11 supergravity which admit a null Killing spinor i.e. a Killing spinor which can be used to construct a null Killing vector. This class covers all supersymmetric time-dependent configurations and completes the classification of the most general supersymmetric configurations initiated in hep-th/0212008.Comment: 30 pages, typos corrected, reference added, new solution included in section 5.1; uses JHEP3.cl

Toward NS5 Branes on the Resolved Cone over Y^{p,q}

Motivated by recent developments in the understanding of the connection between five branes on resolved geometries and the corresponding generalizations of complex deformations in the context of the warped resolved deformed conifold, we consider the construction of five branes solutions on the resolved cone over Y^{p,q} spaces. We establish the existence of supersymmetric five branes solutions wrapped on two-cycles of the resolved cone over Y^{p,q} in the probe limit. We then use calibration techniques to begin the construction of fully back-reacted five branes; we present an Ansatz and the corresponding equations of motion. Our results establish a detailed framework to study back-reacted five branes wrapped on the resolved cone over Y^{p,q} and as a first step we find explicit solutions and construct an asymptotic expansion with the expected properties.Comment: 23+17pp, no figures; v2: references added, various clarification

The Backreacted K\"ahler Geometry of Wrapped Branes

For supersymmetric solutions of D3(M2) branes with AdS3(AdS2) factor, it is known that the internal space is expressible as U(1) fibration over K\"ahler space which satisfies a specific partial differential equation involving the Ricci tensor. In this paper we study the wrapped brane solutions of D3 and M2-branes which were originally constructed using gauged supergravity and uplifted to D=10 and D=11. We rewrite the solutions in canonical form, identify the backreacted K\"ahler geometry, and present a class of solutions which satisfy the Killing spinor equation.Comment: v2: 13 pages, refs adde

On the smoothness of the multi-BMPV black hole spacetime

We demonstrate that, in a multi-BMPV black hole spacetime, the event horizon is not smooth. We explicitly show that for a simpler configuration comprising a line of static extremal black holes and a single BMPV black hole, the metric at the horizon of the BMPV black hole is once, but not twice, continuously differentiable. We argue that this result is also valid when all the black holes are rotating. The Maxwell field strength is shown to be continuous, but not differentiable at the horizon. We also briefly demonstrate that previous work done to show lack of smoothness of static multi-centre solutions in five dimensions is not significantly modified by the inclusion of a higher derivative term in the action for five dimensional supergravity.Comment: 17 pages; reference adde

Brane Resolution Through Fibration

We consider p-branes with one or more circular directions fibered over the transverse space. The fibration, in conjunction with the transverse space having a blown-up cycle, enables these p-brane solutions to be completely regular. Some such circularly-wrapped D3-brane solutions describe flows from SU(N)^3 N=2 theory, F_0 theory, as well as an infinite family of superconformal quiver gauge theories, down to three-dimensional field theories. We discuss the operators that are turned on away from the UV fixed points. Similarly, there are wrapped M2-brane solutions which describe smooth flows from known three-dimensional supersymmetric Chern-Simons matter theories, such as ABJM theory. We also consider p-brane solutions on gravitational instantons, and discuss various ways in which U-duality can be applied to yield other non-singular solutions.Comment: 35 pages, additional referenc

Beyond LLM in M-theory

The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent Killing directions when a general Killing spinor ansatz is considered. Here we show that these directions always commute, identify when the Killing spinors are charged, and show that both their inner product and resulting geometry are governed by two fundamental constants. In particular, setting one constant to zero leads to AdS7 x S4, setting the other to zero gives AdS4 x S7, while flat spacetime is recovered when both these constants are zero. Furthermore, when the constants are equal, the spacetime is either LLM, or it corresponds to the Kowalski-Glikman solution where the constants are simply the mass parameter.Comment: 1+30 pages, footnote adde