The geometry of extended null supersymmetry in M-theory

For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and sufficient conditions are comprised of algebraic relationships, linear in the spinorial components, between the spinorial components and their first derivatives, and the components of the spin connection and four-form. The integrability conditions for the Killing spinor equation are also analysed in detail, to determine which components of the field equations are implied by arbitrary additional supersymmetries and the four-form Bianchi identity. This provides a complete formalism for the systematic and exhaustive investigation of all spacetimes with extended null supersymmetry in eleven dimensions. The formalism is employed to show that the general bosonic solution of eleven dimensional supergravity admitting a $G_2$ structure defined by four Killing spinors is either locally the direct product of $\mathbb{R}^{1,3}$ with a seven-manifold of $G_2$ holonomy, or locally the Freund-Rubin direct product of $AdS_4$ with a seven-manifold of weak $G_2$ holonomy. In addition, all supersymmetric spacetimes admitting a $(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2$ structure are classified.Comment: 36 pages, latex; v2, section classifying all spacetimes admitting a $(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2$ structure included; v3, typos corrected. Final version to appear in Phys.Rev.

Calibrated Entanglement Entropy

The Ryu-Takayanagi prescription reduces the problem of calculating entanglement entropy in CFTs to the determination of minimal surfaces in a dual anti-de Sitter geometry. For 3D gravity theories and BTZ black holes, we identify the minimal surfaces as special Lagrangian cycles calibrated by the real part of the holomorphic one-form of a spacelike hypersurface. We show that (generalised) calibrations provide a unified way to determine holographic entanglement entropy from minimal surfaces, which is applicable to warped AdS$_3$ geometries. We briefly discuss generalisations to higher dimensions.Comment: v1 22 pages, 1 figure; v2 appendix improved and moved into the body to show the application of calibrations to find minimal surfaces in warped AdS, matches published versio

Mapping the G-structures and supersymmetric vacua of five-dimensional N=4 supergravity

We classify the supersymmetric vacua of N=4, d=5 supergravity in terms of G-structures. We identify three classes of solutions: with R^3, SU(2) and generic SO(4) structure. Using the Killing spinor equations, we fully characterize the first two classes and partially solve the latter. With the N=4 graviton multiplet decomposed in terms of N=2 multiplets: the graviton, vector and gravitino multiplets, we obtain new supersymmetric solutions corresponding to turning on fields in the gravitino multiplet. These vacua are described in terms of an SO(5) vector sigma-model coupled with gravity, in three or four dimensions. A new feature of these N=4 vacua, which is not seen from an N=2 point of view, is the possibility for preserving more exotic fractions of supersymmetry. We give a few concrete examples of these new supersymmetric (albeit singular) solutions. Additionally, we show how by truncating the N=4, d=5 set of fields to minimal supergravity coupled with one vector multiplet we recover the known two-charge solutions.Comment: 31 pages, late

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

M-Horizons

We solve the Killing spinor equations and determine the near horizon geometries of M-theory that preserve at least one supersymmetry. The M-horizon spatial sections are 9-dimensional manifolds with a Spin(7) structure restricted by geometric constraints which we give explicitly. We also provide an alternative characterization of the solutions of the Killing spinor equation, utilizing the compactness of the horizon section and the field equations, by proving a Lichnerowicz type of theorem which implies that the zero modes of a Dirac operator coupled to 4-form fluxes are Killing spinors. We use this, and the maximum principle, to solve the field equations of the theory for some special cases and present some examples.Comment: 36 pages, latex. Reference added, minor typos correcte

Probing partially localized supergravity background of fundamental string ending on Dp-brane

We study the dynamics of the probe fundamental string in the field background of the partially localized supergravity solution for the fundamental string ending on Dp-brane. We separately analyze the probe dynamics for its motion along the worldvolume direction and the transverse direction of the source Dp-brane. We compare the dynamics of the probe along the Dp-brane worldvolume direction to the BIon dynamics.Comment: 20 pages, LaTeX, revised version to appear in Phys. Rev.

Bubbling AdS Black Holes

We explore the non-BPS analog of `AdS bubbles', which are regular spherically symmetric 1/2 BPS geometries in type IIB supergravity. They have regular horizons and can be thought of as bubbling generalizations of non-extremal AdS black hole solutions in five-dimensional gauged supergravity. Due to the appearance of the Heun equation even at the linearized level, various approximation and numerical methods are needed in order to extract information about this system. We study how the vacuum expectation value and mass of a particular dimension two chiral primary operator depend on the temperature and chemical potential of the thermal Yang-Mills theory. In addition, the mass of the bubbling AdS black holes is computed. As is shown numerically, there are also non-BPS solitonic bubbles which are completely regular and arise from continuous deformations of BPS AdS bubbles.Comment: 37 pages, 2 figure

Toric Kahler metrics and AdS_5 in ring-like co-ordinates

Stationary, supersymmetric supergravity solutions in five dimensions have Kahler metrics on the four-manifold orthogonal to the orbits of a time-like Killing vector. We show that an explicit class of toric Kahler metrics provide a unified framework in which to describe both the asymptotically flat and asymptotically AdS solutions. The Darboux co-ordinates used for the local description turn out to be ''ring-like.'' We conclude with an Ansatz for studying the existence of supersymmetric black rings in AdS.Comment: A new appendix derives the explicit co-ordinate transformation between the ``ring-like'' co-ordinates and the polar co-ordinates of global AdS. Also, references adde

Brane Solitons for G_2 Structures in Eleven-Dimensional Supergravity Re-Visited

We investigate the four-dimensional supergravity theory obtained from the compactification of eleven-dimensional supergravity on a smooth manifold of G_2 holonomy. We give a new derivation for the Kaehler potential associated with the scalar kinetic term of the N=1 four-dimensional theory. We then examine some solutions of the four-dimensional theory which arise from wrapped M-branes.Comment: 11 Pages, Latex, references adde