AdS spacetimes from wrapped D3-branes

We derive a geometrical characterisation of a large class of AdS_3 and AdS_2 supersymmetric spacetimes in IIB supergravity with non-vanishing five-form flux using G-structures. These are obtained as special cases of a class of supersymmetric spacetimes with an $\mathbb{R}^{1,1}$ or $\mathbb{R}$ (time) factor that are associated with D3-branes wrapping calibrated 2- or 3- cycles, respectively, in manifolds with SU(2), SU(3), SU(4) and G_2 holonomy. We show how two explicit AdS solutions, previously constructed in gauged supergravity, satisfy our more general G-structure conditions. For each explicit solution we also derive a special holonomy metric which, although singular, has an appropriate calibrated cycle. After analytic continuation, some of the classes of AdS spacetimes give rise to known classes of BPS bubble solutions with $\mathbb{R}\times SO(4)\times SO(4)$, $\mathbb{R}\times SO(4)\times U(1)$, and $\mathbb{R}\times SO(4)$ symmetry. These have 1/2, 1/4 and 1/8 supersymmetry, respectively. We present a new class of 1/8 BPS geometries with $\mathbb{R}\times SU(2)$ symmetry, obtained by analytic continuation of the class of AdS spacetimes associated with D3-branes wrapped on associative three-cycles.Comment: 1+30 pages; v2, references added; v3, typos corrected, reference adde

Systematics of M-theory spinorial geometry

We reduce the classification of all supersymmetric backgrounds in eleven dimensions to the evaluation of the supercovariant derivative and of an integrability condition, which contains the field equations, on six types of spinors. We determine the expression of the supercovariant derivative on all six types of spinors and give in each case the field equations that do not arise as the integrability conditions of Killing spinor equations. The Killing spinor equations of a background become a linear system for the fluxes, geometry and spacetime derivatives of the functions that determine the spinors. The solution of the linear system expresses the fluxes in terms of the geometry and specifies the restrictions on the geometry of spacetime for all supersymmetric backgrounds. We also show that the minimum number of field equations that is needed for a supersymmetric configuration to be a solution of eleven-dimensional supergravity can be found by solving a linear system. The linear systems of the Killing spinor equations and their integrability conditions are given in both a timelike and a null spinor basis. We illustrate the construction with examples.Comment: 46 pages. v2: systematics of a null spinor basis is included in section

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

The spinorial geometry of supersymmetric backgrounds

We propose a new method to solve the Killing spinor equations of eleven-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1,10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for N=2 backgrounds provided that one of the spinors represents the orbit of Spin(1,10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N=1 and some N=2, N=3 and N=4 backgrounds. In the N=2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N=2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N=2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure and the latter leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds with extended, N>2, supersymmetry. We investigate a class of N=3 and N=4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi-Yau compactifications with fluxes to one-dimension.Comment: Latex, 54 pages, v2: clarifications made and references added. v3: minor changes. v4: minor change

1/2-BPS states in M theory and defects in the dual CFTs

We study supersymmetric branes in AdS_7 x S^4 and AdS_4 x S^7. We show that in the former case the membranes should be viewed as M5 branes with fluxes and we identify two types of such fivebranes (they are analogous to giant gravitons and to dual giants). In AdS_4 x S^7 we find both M5 branes with fluxes and freestanding stacks of membranes. We also go beyond probe approximation and construct regular supergravity solutions describing geometries produced by the branes. The metrics are completely specified by one function which satisfies either Laplace or Toda equation and we give a complete classification of boundary conditions leading to smooth geometries. The brane configurations discussed in this paper are dual to various defects in three- and six-dimensional conformal field theories.Comment: 82 pages, 12 figures, added ref