33 research outputs found
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 structure defined by four Killing
spinors is either locally the direct product of with a
seven-manifold of holonomy, or locally the Freund-Rubin direct product of
with a seven-manifold of weak holonomy. In addition, all
supersymmetric spacetimes admitting a
structure are classified.Comment: 36 pages, latex; v2, section classifying all spacetimes admitting a
structure included; v3, typos
corrected. Final version to appear in Phys.Rev.
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 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
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
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 or (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
, , 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-branes wrapped on associative
three-cycles.Comment: 1+30 pages; v2, references added; v3, typos corrected, reference
adde
AdS spacetimes from wrapped M5 branes
We derive a complete geometrical characterisation of a large class of
, and supersymmetric spacetimes in eleven-dimensional
supergravity using G-structures. These are obtained as special cases of a class
of supersymmetric , and
geometries, naturally associated to M5-branes wrapping calibrated cycles in
manifolds with , 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
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
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 manifolds; complex
lagrangian four-cycles in manifolds; and Cayley four-cycles in
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 metrics on an
bundle over , and an bundle over or ;
the Calabi hyper-K\"{a}hler metric on ; and the
Bryant-Salamon-Gibbons-Page-Pope metric on an bundle
over . 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
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 to 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. Bosonic fluxes introduce torsion terms that
deform the structure away from a covariantly
constant one. The most general structure can be classified in 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
K\"{a}hler, 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 supersymmetric solutions; we show that the U(1) theory admits a symmetric
Cahen-Wallach solution together with a compactifying pp-wave. The
SU(2) theory admits a black string, whose near horizon limit is . We also obtain the Yang-Mills analogue of the Salam-Sezgin solution of
the U(1) theory, namely , where the is supported by a
sphaleron. Finally we obtain the additional constraints implied by enhanced
supersymmetry, and discuss Penrose limits in the theories.Comment: 1+29 pages, late