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Invariant Killing spinors in 11D and type II supergravities
We present all isotropy groups and associated groups, up to discrete
identifications of the component connected to the identity, of spinors of
eleven-dimensional and type II supergravities. The groups are products
of a Spin group and an R-symmetry group of a suitable lower dimensional
supergravity theory. Using the case of SU(4)-invariant spinors as a paradigm,
we demonstrate that the groups, and so the R-symmetry groups of
lower-dimensional supergravity theories arising from compactifications, have
disconnected components. These lead to discrete symmetry groups reminiscent of
R-parity. We examine the role of disconnected components of the groups
in the choice of Killing spinor representatives and in the context of
compactifications.Comment: 22 pages, typos correcte
Supersymmetric geometries of IIA supergravity I
IIA supergravity backgrounds preserving one supersymmetry locally admit four
types of Killing spinors distinguished by the orbits of on the
space of spinors. We solve the Killing spinor equations of IIA supergravity
with and without cosmological constant for Killing spinors representing two of
these orbits, with isotropy groups and .
In both cases, we identify the geometry of spacetime and express the fluxes in
terms of the geometry. We find that the geometric constraints of backgrounds
with a invariant Killing spinor are identical to
those found for heterotic backgrounds preserving one supersymmetry.Comment: 21 page
IIB backgrounds with five-form flux
We investigate all N=2 supersymmetric IIB supergravity backgrounds with
non-vanishing five-form flux. The Killing spinors have stability subgroups
Spin(7)\ltimes\bR^8, SU(4)\ltimes\bR^8 and . In the
SU(4)\ltimes\bR^8 case, two different types of geometry arise depending on
whether the Killing spinors are generic or pure. In both cases, the backgrounds
admit a null Killing vector field which leaves invariant the SU(4)\ltimes
\bR^8 structure, and an almost complex structure in the directions transverse
to the lightcone. In the generic case, the twist of the vector field is trivial
but the almost complex structure is non-integrable, while in the pure case the
twist is non-trivial but the almost complex structure is integrable and
associated with a relatively balanced Hermitian structure. The
backgrounds admit a time-like Killing vector field and two spacelike closed
one-forms, and the seven directions transverse to these admit a co-symplectic
structure. The Spin(7)\ltimes\bR^8 backgrounds are pp-waves propagating
in an eight-dimensional manifold with holonomy . In addition we show
that all the supersymmetric solutions of simple five-dimensional supergravity
with a time-like Killing vector field, which include the black holes,
lift to SU(4)\ltimes\bR^8 pure Killing spinor IIB backgrounds. We also show
that the LLM solution is associated with a co-symplectic co-homogeneity one
manifold which has principal orbit .Comment: 39 pages, typos corrected and references amende
Geometry of all supersymmetric four-dimensional supergravity backgrounds
We solve the Killing spinor equations of supergravity, with four
supercharges, coupled to any number of vector and scalar multiplets in all
cases. We find that backgrounds with N=1 supersymmetry admit a null,
integrable, Killing vector field. There are two classes of N=2 backgrounds. The
spacetime in the first class admits a parallel null vector field and so it is a
pp-wave. The spacetime of the other class admits three Killing vector fields,
and a vector field that commutes with the three Killing directions. These
backgrounds are of cohomogeneity one with homogenous sections either
\bR^{2,1} or and have an interpretation as domain walls. The N=3
backgrounds are locally maximally supersymmetric. There are N=3 backgrounds
which arise as discrete identifications of maximally supersymmetric ones. The
maximally supersymmetric backgrounds are locally isometric to either
\bR^{3,1} or .Comment: 15 pages; minor changes, references added, published versio
Index theory and dynamical symmetry enhancement near IIB horizons
We show that the number of supersymmetries of IIB black hole horizons is N=2
N_- + 2 index(D_\lambda), where index(D_\lambda) is the index of the Dirac
operator twisted with the line bundle \lambda^{1/2} of IIB scalars, and N_- is
the dimension of the kernel of a horizon Dirac operator which depends on IIB
fluxes. Therefore, all IIB horizons preserve an even number of supersymmetries.
In addition if the horizons have non-trivial fluxes and N_- is nonzero, then
index(D_\lambda) is non-negative, and the horizons admit an sl(2,R) symmetry
subalgebra. This provides evidence that all such horizons have an AdS/CFT dual.
Furthermore if the orbits of sl(2,R) are two-dimensional, the IIB horizons are
warped products AdS_2 X S.Comment: 37 pages, late
IIB black hole horizons with five-form flux and extended supersymmetry
We classify under some assumptions the IIB black hole horizons with 5-form
flux preserving more than 2 supersymmetries. We find that the spatial horizon
sections with non-vanishing flux preserving 4 supersymmetries are locally
isometric either to S^1 * S^3 * T^4 or to S^1 * S^3 * K_3 and the associated
near horizon geometries are locally isometric to AdS_3 * S^3 * T^4 and AdS_3 *
S^3 * K_3$, respectively. The near horizon geometries preserving more than 4
supersymmetries are locally isometric to R^{1,1} * T^8.Comment: 16 pages, latex. Minor typos correcte
M-theory backgrounds with 30 Killing spinors are maximally supersymmetric
We show that all M-theory backgrounds which admit more than 29 Killing
spinors are maximally supersymmetric. In particular, we find that the
supercovariant curvature of all backgrounds which preserve 30 supersymmetries,
subject to field equations and Bianchi identities, vanishes, and that there are
no such solutions which arise as discrete quotients of maximally supersymmetric
backgrounds.Comment: 37 pages, latex. Minor changes
Classification of IIB backgrounds with 28 supersymmetries
We show that all IIB backgrounds with strictly 28 supersymmetries are locally
isometric to the plane wave solution of arXiv:hep-th/0206195. Moreover, we
demonstrate that all solutions with more than 26 supersymmetries and only
5-form flux are maximally supersymmetric. The N=28 plane wave solution is a
superposition of the maximally supersymmetric IIB plane wave with a heterotic
string solution. We investigate the propagation of strings in this background,
find the spectrum and give the string light-cone Hamiltonian.Comment: 30 pages, typos correcte
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