13 research outputs found
The Geometry of D=11 Killing Spinors
We propose a way to classify all supersymmetric configurations of D=11
supergravity using the G-structures defined by the Killing spinors. We show
that the most general bosonic geometries admitting a Killing spinor have at
least a local SU(5) or an (Spin(7)\ltimes R^8)x R structure, depending on
whether the Killing vector constructed from the Killing spinor is timelike or
null, respectively. In the former case we determine what kind of local SU(5)
structure is present and show that almost all of the form of the geometry is
determined by the structure. We also deduce what further conditions must be
imposed in order that the equations of motion are satisfied. We illustrate the
formalism with some known solutions and also present some new solutions
including a rotating generalisation of the resolved membrane solutions and
generalisations of the recently constructed D=11 Godel solution.Comment: 36 pages. Typos corrected and discussion on G-structures improved.
Final version to appear in JHE
New non compact Calabi-Yau metrics in D=6
A method for constructing explicit Calabi-Yau metrics in six dimensions in
terms of an initial hyperkahler structure is presented. The equations to solve
are non linear in general, but become linear when the objects describing the
metric depend on only one complex coordinate of the hyperkahler 4-dimensional
space and its complex conjugated. This situation in particular gives a dual
description of D6-branes wrapping a complex 1-cycle inside the hyperkahler
space, which was studied by Fayyazuddin. The present work generalize the
construction given by him. But the explicit solutions we present correspond to
the non linear problem. This is a non linear equation with respect to two
variables which, with the help of some specific anzatz, is reduced to a non
linear equation with a single variable solvable in terms of elliptic functions.
In these terms we construct an infinite family of non compact Calabi-Yau
metrics.Comment: A numerical error has been corrected together with the corresponding
analysis of the metri
Type IIB Theory on Half-flat Manifolds
In this note we derive the low-energy effective action of type IIB theory
compactified on half-flat manifolds and we show that this precisely coincides
with the low-energy effective action of type IIA theory compactified on a
Calabi-Yau manifold in the presence of NS three-form fluxes. We provide in this
way a further check of the recently formulated conjecture that half-flat
manifolds appear as mirror partners of Calabi-Yau manifolds when NS fluxes are
turned on.Comment: 15 pages, no figure
Heterotic compactifications on SU(2)-structure backgrounds
In this paper we study the reduction of heterotic string theory on
SU(2)-structure backgrounds. We compute the bosonic low-energy gauged N=2
supergravity specified by the Killing vectors corresponding to the gauged
isometries. We check that the obtained Lagrangian is consistent with the one of
N=2 local supersymmetry. We also determine the Killing prepotentials.Comment: reference added, corrected typos and some factor
E7(7) formulation of N=2 backgrounds
In this paper we reformulate N=2 supergravity backgrounds arising in type II
string theory in terms of quantities transforming under the U-duality group
E7(7). In particular we combine the Ramond--Ramond scalar degrees of freedom
together with the O(6,6) pure spinors which govern the Neveu-Schwarz sector by
considering an extended version of generalised geometry. We give
E7(7)-invariant expressions for the Kahler and hyperkahler potentials
describing the moduli space of vector and hypermultiplets, demonstrating that
both correspond to standard E7(7) coset spaces. We also find E7(7) expressions
for the Killing prepotentials defining the scalar potential, and discuss the
equations governing N=1 vacua in this formalism.Comment: 40 pages, final version to appear in JHE
Type IIA orientifold compactification on SU(2)-structure manifolds
We investigate the effective theory of type IIA string theory on
six-dimensional orientifold backgrounds with SU(2)-structure. We focus on the
case of orientifolds with O6-planes, for which we compute the bosonic effective
action in the supergravity approximation. For a generic SU(2)-structure
background, we find that the low-energy effective theory is a gauged N=2
supergravity where moduli in both vector and hypermultiplets are charged. Since
all these supergravities descend from a corresponding N=4 background, their
scalar target space is always a quotient of a SU(1,1)/U(1) x
SO(6,n)/SO(6)xSO(n) coset, and is therefore also very constrained.Comment: 31 pages; v2: local report number adde
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