44 research outputs found
N=31, D=11
We show that eleven-dimensional supergravity backgrounds with thirty one
supersymmetries, N=31, admit an additional Killing spinor and so they are
locally isometric to maximally supersymmetric ones. This rules out the
existence of simply connected eleven-dimensional supergravity preons. We also
show that N=15 solutions of type I supergravities are locally isometric to
Minkowski spacetime.Comment: 17 page
IIB solutions with N>28 Killing spinors are maximally supersymmetric
We show that all IIB supergravity backgrounds which admit more than 28
Killing spinors are maximally supersymmetric. In particular, we find that for
all N>28 backgrounds the supercovariant curvature vanishes, and that the
quotients of maximally supersymmetric backgrounds either preserve all 32 or
N<29 supersymmetries.Comment: 27 page
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
The return of the four- and five-dimensional preons
We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged
supergravities by explicitly constructing them as smooth quotients of the AdS_4
and AdS_5 maximally supersymmetric backgrounds, respectively. This result
illustrates how the spacetime topology resurrects a fraction of supersymmetry
previously ruled out by the local analysis of the Killing spinor equations.Comment: 10 pages (a minor imprecision has been corrected
The holonomy of IIB supercovariant connection
We show that the holonomy of the supercovariant connection of IIB
supergravity is contained in SL(32, \bR). We also find that the holonomy
reduces to a subgroup of SL(32-N)\st (\oplus^N \bR^{32-N}) for IIB
supergravity backgrounds with Killing spinors. We give the necessary and
sufficient conditions for a IIB background to admit Killing spinors. A IIB
supersymmetric probe configuration can involve up to 31 linearly independent
planar branes and preserves one supersymmetry.Comment: 8 pages, latex. v2: Minor correction
On the maximal superalgebras of supersymmetric backgrounds
In this note we give a precise definition of the notion of a maximal
superalgebra of certain types of supersymmetric supergravity backgrounds,
including the Freund-Rubin backgrounds, and propose a geometric construction
extending the well-known construction of its Killing superalgebra. We determine
the structure of maximal Lie superalgebras and show that there is a finite
number of isomorphism classes, all related via contractions from an
orthosymplectic Lie superalgebra. We use the structure theory to show that
maximally supersymmetric waves do not possess such a maximal superalgebra, but
that the maximally supersymmetric Freund-Rubin backgrounds do. We perform the
explicit geometric construction of the maximal superalgebra of AdS_4 x S^7 and
find that is isomorphic to osp(1|32). We propose an algebraic construction of
the maximal superalgebra of any background asymptotic to AdS_4 x S^7 and we
test this proposal by computing the maximal superalgebra of the M2-brane in its
two maximally supersymmetric limits, finding agreement.Comment: 17 page
Parallelisable Heterotic Backgrounds
We classify the simply-connected supersymmetric parallelisable backgrounds of
heterotic supergravity. They are all given by parallelised Lie groups admitting
a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14
and 16 of the 16 supersymmetries.Comment: 17 pages, AMSLaTe
The spinorial geometry of supersymmetric heterotic string backgrounds
We determine the geometry of supersymmetric heterotic string backgrounds for
which all parallel spinors with respect to the connection with
torsion , the NSNS three-form field strength, are Killing. We find
that there are two classes of such backgrounds, the null and the timelike. The
Killing spinors of the null backgrounds have stability subgroups
K\ltimes\bR^8 in , for , SU(4), , and , and the Killing spinors of the timelike backgrounds have
stability subgroups , SU(3), SU(2) and . The former admit a single
null -parallel vector field while the latter admit a timelike and
two, three, five and nine spacelike -parallel vector fields,
respectively. The spacetime of the null backgrounds is a Lorentzian
two-parameter family of Riemannian manifolds with skew-symmetric torsion.
If the rotation of the null vector field vanishes, the holonomy of the
connection with torsion of is contained in . The spacetime of time-like
backgrounds is a principal bundle with fibre a Lorentzian Lie group and
base space a suitable Riemannian manifold with skew-symmetric torsion. The
principal bundle is equipped with a connection which determines the
non-horizontal part of the spacetime metric and of . The curvature of
takes values in an appropriate Lie algebra constructed from that of
. In addition has only horizontal components and contains the
Pontrjagin class of . We have computed in all cases the Killing spinor
bilinears, expressed the fluxes in terms of the geometry and determine the
field equations that are implied by the Killing spinor equations.Comment: 73pp. v2: minor change
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
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