A Brane Teaser

In this note we study the puzzle posed by two M5-branes intersecting on a string (or equivalently, a single M5-brane wrapping a holomorphic four-cycle in C^4). It has been known for a while that this system is different from all other configurations built using self-intersecting M-branes; in particular the corresponding supergravity solution exhibits various curious features which have remained unexplained. We propose that the resolution to these puzzles lies in the existence of a non-zero two-form on the M5-brane world-volume.Comment: 21 pages. References adde

That's a wrap!

Calibration technology provides us with a fast and elegant way to find the supergravity solutions for BPS wrapped M-branes. Its true potential had however remained untapped due to the absence of a classification of calibrations in spacetimes with non-trivial flux. The applications of this method were thus limited in practise to M-branes wrapping Kahler calibrated cycles. In this paper, we catagorize a type of generalised calibrations which exist in supergravity backgrounds and contain Kahler calibrations as a sub-class. This broadens the arena of brane configurations whose supergravity solutions are accessible through the calibration 'short-cut' method.Comment: 19 pages, typos correcte

M2-branes wrapped on holomorphic curves

The generalised calibration for a wrapped membrane is gauge equivalent to the supergravity three-form under which the membrane is electrically charged. Given the relevant calibration, one can go a long way towards constructing the supergravity solution for the wrapped brane. Applications of this method have been restricted since generalised calibrations have not yet been completely classified in spacetimes with non-vanishing flux. In this paper, we take a first step towards such a classification by studying membranes wrapping holomorphic curves. Supersymmetry preservation imposes a constraint on the Hermitean metric in the embedding space and it is found that this can be expressed as a restriction on possible generalised calibrations. Allowed calibrations in a particular spacetime are simply those which satisfy the constraint equation relevant to that background; in particular, we see that the previously considered Kahler calibrations are just a subclass of possible solutions.Comment: Discussion clarified, typos corrected, references updated. Results remain unchanged. 12 page

AdS spacetimes from wrapped M5 branes

We derive a complete geometrical characterisation of a large class of $AdS_3$, $AdS_4$ and $AdS_5$ supersymmetric spacetimes in eleven-dimensional supergravity using G-structures. These are obtained as special cases of a class of supersymmetric $\mathbb{R}^{1,1}$, $\mathbb{R}^{1,2}$ and $\mathbb{R}^{1,3}$ geometries, naturally associated to M5-branes wrapping calibrated cycles in manifolds with $G_2$, SU(3) or SU(2) holonomy. Specifically, the latter class is defined by requiring that the Killing spinors satisfy the same set of projection conditions as for wrapped probe branes, and that there is no electric flux. We show how the R-symmetries of the dual field theories appear as isometries of the general AdS geometries. We also show how known solutions previously constructed in gauged supergravity satisfy our more general G-structure conditions, demonstrate that our conditions for half-BPS $AdS_5$ geometries are precisely those of Lin, Lunin and Maldacena, and construct some new singular solutions.Comment: 1+56 pages, LaTeX; v2, references added; v3, minor corrections, final version to appear in JHE

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

Exact Solutions of Open Bosonic String Field Theory

In this paper we present two solutions of open bosonic string field theory defined on D0-brane background that correspond to the change of the D0-brane position in the transverse space.Comment: 18 page

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

N=1 M5-brane geometries

We describe how to construct solutions to eleven-dimensional supergravity corresponding to M5-branes wrapped on holomorphic 2-cycles embedded in 3. These solutions preserve = 1 supersymmetry in four dimensions. In the near-horizon limit they are expected to be dual to = 1 large-N gauge theories in four dimensions by Maldacena's duality