1,186 research outputs found
Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces
Heterotic horizons preserving 4 supersymmetries have sections which are T^2
fibrations over 6-dimensional conformally balanced Hermitian manifolds. We give
new examples of horizons with sections S^3 X S^3 X T^2 and SU(3). We then
examine the heterotic horizons which are T^4 fibrations over a Kahler
4-dimensional manifold. We prove that the solutions depend on 6 functions which
are determined by a non-linear differential system of 6 equations that include
the Monge-Ampere equation. We show that this system has an explicit solution
for the Kahler manifold S^2 X S^2. We also demonstrate that there is an
associated cohomological system which has solutions on del Pezzo surfaces. We
raise the question of whether for every solution of the cohomological problem
there is a solution of the differential system, and so a new heterotic horizon.
The horizon sections have topologies which include ((k-1) S^2 X S^4 # k (S^3 X
S^3)) X T^2$ indicating the existence of exotic black holes. We also find an
example of a horizon section which gives rise to two different near horizon
geometries.Comment: 33 pages, latex. Reference adde
Index theory and dynamical symmetry enhancement of M-horizons
We show that near-horizon geometries of 11-dimensional supergravity preserve
an even number of supersymmetries. The proof follows from Lichnerowicz type
theorems for two horizon Dirac operators, the field equations and Bianchi
identities, and the vanishing of the index of a Dirac operator on the
9-dimensional horizon sections. As a consequence of this, we also prove that
all M-horizons with non-vanishing fluxes admit a sl(2,R) subalgebra of
symmetries.Comment: Minor typos corrected. 22 pages, latex. Repeats equations and
descriptions from arXiv:1207.708
On supersymmetric AdS6 solutions in 10 and 11 dimensions
We prove a non-existence theorem for smooth, supersymmetric, warped AdS6
solutions with connected, compact without boundary internal space in D=11 and
(massive) IIA supergravities. In IIB supergravity we show that if such AdS6
solutions exist, then the NSNS and RR 3-form fluxes must be linearly
independent and certain spinor bi-linears must be appropriately restricted.
Moreover we demonstrate that the internal space admits an so(3) action which
leaves all the fields invariant and for smooth solutions the principal orbits
must have co-dimension two. We also describe the topology and geometry of
internal spaces that admit such a so(3) action and show that there are no
solutions for which the internal space has topology F * S^2, where F is an
oriented surface.Comment: 26 pages, late
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 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
Deformations of generalized calibrations and compact non-Kahler manifolds with vanishing first Chern class
We investigate the deformation theory of a class of generalized calibrations
in Riemannian manifolds for which the tangent bundle has reduced structure
group U(n), SU(n), G_2 and Spin(7). For this we use the property of the
associated calibration form to be parallel with respect to a metric connection
which may have non-vanishing torsion. In all these cases, we find that if there
is a moduli space, then it is finite dimensional.
We present various examples of generalized calibrations that include almost
hermitian manifolds with structure group U(n) or SU(n), nearly parallel G_2
manifolds and group manifolds. We find that some Hopf fibrations are
deformation families of generalized calibrations. In addition, we give
sufficient conditions for a hermitian manifold (M,g,J) to admit Chern and
Bismut connections with holonomy contained in SU(n). In particular we show that
any connected sum of copies of admits a hermitian
structure for which the restricted holonomy of a Bismut connection is contained
in SU(3).Comment: 43 pages, Latex, typos corrected, reference added in section
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
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