Oisin A. P. Mac Conamhna

The general form of supersymmetric solutions of N = (1, 0) U(1) and SU(2) gauged supergravities in six dimensions

We obtain necessary and sufficient conditions for a supersymmetric field configuration in the N = (1, 0) U(1) or SU(2) gauged supergravities in six dimensions, and impose the field equations on this general ansatz. It is found that any supersymmetric solution is associated with an structure. The structure is characterized by a null Killing vector which induces a natural 2 + 4 split of the six-dimensional spacetime. A suitable combination of the field equations implies that the scalar curvature of the four-dimensional Riemannian part, referred to as the base, obeys a second-order differential equation; surprisingly, for a large class of solutions the equation in the SU(2) theory requires the vanishing of the Weyl anomaly of N = 4 SYM on the base. Bosonic fluxes introduce torsion terms that deform the structure away from a covariantly constant one. The most general structure can be classified into terms of its intrinsic torsion. For a large class of solutions the gauge field strengths admit a simple geometrical interpretation: in the U(1) theory the base is Kahler, and the gauge field strength is the Ricci form; in the SU(2) theory, the gauge field strengths are identified with the curvatures of the left-hand spin bundle of the base. We employ our general ansatz to construct new solutions; we show that the U(1) theory admits a symmetric Cahen–Wallach4 × S2 solution together with a compactifying pp-wave. The SU(2) theory admits a black string, whose near horizon limit is AdS3 × S3, which is supported by a self-dual 3-form flux and a meron on the S3. In the limit of the zero 3-form flux we obtain the Yang–Mills analogue of the Salam–Sezgin solution of the U(1) theory, namely R1,2 × S3. Finally we obtain the additional constraints implied by enhanced supersymmetry, and discuss Penrose limits in the theories.

AdS spacetimes from wrapped M5 branes

We derive a complete geometrical characterisation of a large class of AdS3, AdS4 and AdS5 supersymmetric spacetimes in eleven-dimensional supergravity using G-structures. These are obtained as special cases of a class of supersymmetric 1,1, 1,2 and 1,3 geometries, naturally associated to M5-branes wrapping calibrated cycles in manifolds with G2, 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 AdS5 geometries are precisely those of Lin, Lunin and Maldacena, and construct some new singular solutions.

AdS spacetimes from wrapped D3-branes

We derive a geometrical characterization of a large class of AdS3 and AdS2 supersymmetric spacetimes in type 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 or (time) factor that are associated with D3 branes wrapping calibrated two or three cycles, respectively, in manifolds with SU(2), SU(3), SU(4) and G2 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 and symmetry. These have 1/2, 1/4 and 1/8 supersymmetry, respectively. We present a new class of 1/8 BPS geometries with symmetry, obtained by analytic continuation of the class of AdS spacetimes associated with D3-brane wrapped on associative three cycles.

New supersymmetric AdS3 solutions

We construct infinite new classes of supersymmetric solutions of D=11 supergravity that are warped products of AdS{sub 3} with an eight-dimensional manifold M{sub 8} and have nonvanishing four-form flux. In order to be compact, M{sub 8} is constructed as an S{sup 2} bundle over a six-dimensional manifold B{sub 6} which is either Kaehler-Einstein or a product of Kaehler-Einstein spaces. In the special cases that B{sub 6} contains a two-torus, we also obtain new AdS{sub 3} solutions of type IIB supergravity, with constant dilaton and only five-form flux. Via the anti-de Sitter (AdS)-conformal field theory (CFT) correspondence the solutions with compact M{sub 8} will be dual to two-dimensional conformal field theories with N=(0,2) supersymmetry. Our construction can also describe noncompact geometries and we discuss examples in type IIB which are dual to four-dimensional N=1 superconformal theories coupled to stringlike defects.

Timelike killing spinors in seven dimensions

We employ the G-structure formalism to study supersymmetric solutions of minimal and SU(2) gauged supergravities in seven dimensions admitting Killing spinors with an associated timelike Killing vector. The most general such Killing spinor defines a SU(3) structure. We deduce necessary and sufficient conditions for the existence of a timelike Killing spinor on the bosonic fields of the theories, and find that such configurations generically preserve one out of 16 supersymmetries. Using our general supersymmetric ansatz we obtain numerous new solutions, including squashed or deformed anti-de Sitter solutions of the gauged theory, and a large class of Goedel-like solutions with closed timelike curves.

Supersymmetric 3D Anti-de Sitter Space Solutions of Type IIB Supergravity

For every positively curved Kähler-Einstein manifold in four dimensions, we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS3 with a compact seven-dimensional manifold and have nonvanishing five-form flux. Via the anti-de Sitter/conformal field theory correspondence, the solutions are dual to two-dimensional conformal field theories with (0,2) supersymmetry. The corresponding central charges are rational numbers.

Classification of supersymmetric spacetimes in eleven dimensions

We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of 11-dimensional supergravity. The metric, four-form, and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four-form field equation to ensure that the solution of the Killing spinor equation also satisfies all the field equations, and we give these conditions explicitly.

Global geometry of the supersymmetric AdS 3 / CFT 2 correspondence in M-theory

We study the global geometry of a general class of spacetimes of relevance to the supersymmetric three-dimensional anti-de Sitter space/two-dimensional conformal field theory (AdS{sub 3}/CFT{sub 2}) correspondence in 11-dimensional supergravity. Specifically, we study spacetimes admitting a globally defined R{sup 1,1} frame, a globally defined frame bundle with structure group contained in Spin(7), and an AdS{sub 3} event horizon or conformal boundary. We show how the global frame bundle may be canonically realized by globally defined null sections of the spin bundle, which we use to truncate 11-dimensional supergravity to a gravitational theory of a frame with structure group Spin(7), SU(4), or Sp(2). By imposing an AdS{sub 3} boundary condition on the truncated supergravity equations, we define the geometry of all AdS{sub 3} horizons or boundaries which can be obtained from solutions of these truncations. In the most generic case we study, we reproduce the most general conditions for an AdS{sub 3} manifold in M-theory to admit a Killing spinor. As a consistency check on our definitions of AdS geometries we verify that they are satisfied by known gauged supergravity AdS{sub 3} solutions. We discuss future applications of our results.

Supersymmetric AdS_3 solutions of type IIB supergravity

For every positively curved Kähler-Einstein manifold in four dimensions, we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS3 with a compact seven-dimensional manifold and have nonvanishing five-form flux. Via the anti-de Sitter/conformal field theory correspondence, the solutions are dual to two-dimensional conformal field theories with (0,2) supersymmetry. The corresponding central charges are rational numbers.

Supersymmetric wrapped membranes, AdS2 spaces, and bubbling geometries

We perform a systematic study, in eleven dimensional supergravity, of the geometry of wrapped brane configurations admitting