44 research outputs found
On Certain Kähler Quotients of Quaternionic Kähler Manifolds
We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kähler manifold M which preserves a submanifold N ⊂ M, the quotient M′ =N/A has a natural Kähler structure. We verify that the assumptions on the group action and on the submanifold N ⊂ M are satisfied for a large class of examples obtained from the supergravity c-map. In particular, we find that all quaternionic Kähler manifolds M in the image of the c-map admit an integrable complex structure compatible with the quaternionic structure, such that N ⊂ M is a complex submanifold. Finally, we discuss how the existence of the Kähler structure on M′ is required by the consistency of spontaneous to supersymmetry breakin
Generalized geometry, calibrations and supersymmetry in diverse dimensions
We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d,
preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal
supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in
two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor
equations, that there is a one-to-one correspondence between background
supersymmetry equations in pure-spinor form and D-brane generalized
calibrations; this correspondence had been known to hold in the d = 4 case.
Assuming the correspondence to hold for all d, we list the calibration forms
for all admissible D-branes, as well as the background supersymmetry equations
in pure-spinor form. We find a number of general features, including the
following: The pattern of codimensions at which each calibration form appears
exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations
implies that the internal manifold is generalized Calabi-Yau. Our results are
manifestly invariant under generalized mirror symmetry.Comment: 28 pages, 1 tabl
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
D7-Brane Moduli vs. F-Theory Cycles in Elliptically Fibred Threefolds
We study the space of geometric and open string moduli of type IIB
compactifications from the perspective of complex structure deformations of
F-theory. In order to find a correspondence, we work in the weak coupling limit
and for simplicity focus on compactifications to 6 dimensions. Starting from
the topology of D7-branes and O7-planes, we construct the 3-cycles of the
F-theory threefold. We achieve complete agreement between the degrees of
freedom of the Weierstrass model and the complex structure deformations of the
elliptic Calabi-Yau. All relevant quantities are expressed in terms of the
topology of the base space, allowing us to formulate our results for general
base spaces.Comment: 40 pages, 15 figures, references adde
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
Type II compactifications on manifolds with SU(2) x SU(2) structure
We study compactifications of type II theories on SU(2) x SU(2) structure
manifolds to six, five and four spacetime dimensions. We use the framework of
generalized geometry to describe the NS-NS sector of such compactifications and
derive the structure of their moduli spaces. We show that in contrast to SU(3)
x SU(3) structure compactifications, there is no dynamical SU(2) x SU(2)
structure interpolating between an SU(2) structure and an identity structure.
Furthermore, we formulate type II compactifications on SU(2) x SU(2) structures
in the context of exceptional generalized geometry which makes the U-duality
group manifest and naturally incorporates the scalar degrees of freedom arising
in the Ramond-Ramond sector. Via this formalism we derive the structure of the
moduli spaces as it is expected from N=4 supergravity.Comment: 69 pages, v2 published versio
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
On certain K\"ahler quotients of quaternionic K\"ahler manifolds
We prove that, given a certain isometric action of a two-dimensional Abelian
group A on a quaternionic K\"ahler manifold M which preserves a submanifold
N\subset M, the quotient M'=N/A has a natural K\"ahler structure. We verify
that the assumptions on the group action and on the submanifold N\subset M are
satisfied for a large class of examples obtained from the supergravity c-map.
In particular, we find that all quaternionic K\"ahler manifolds M in the image
of the c-map admit an integrable complex structure compatible with the
quaternionic structure, such that N\subset M is a complex submanifold. Finally,
we discuss how the existence of the K\"ahler structure on M' is required by the
consistency of spontaneous {\cal N}=2 to {\cal N}=1 supersymmetry breaking.Comment: 36 page
Moduli Stabilization and Cosmology of Type IIB on SU(2)-Structure Orientifolds
We consider type IIB flux compactifications on six-dimensional
SU(2)-structure manifolds with O5- and O7-planes. These six-dimensional spaces
allow not only for F_3 and H_3 fluxes but also for F_1 and F_5 fluxes. We
derive the four-dimensional N=1 scalar potential for such compactifications and
present one explicit example of a fully stabilized AdS vacuum with large volume
and small string coupling. We then discuss cosmological aspects of these
compactifications and derive several no-go theorems that forbid dS vacua and
slow-roll inflation under certain conditions. We also study concrete examples
of cosets and twisted tori and find that our no-go theorems forbid dS vacua and
slow-roll inflation in all but one of them. For the latter we find a dS
critical point with \epsilon numerically zero. However, the point has two
tachyons and eta-parameter \eta \approx -3.1.Comment: 35 pages + appendices, LaTeX2e; v2: numerical dS extremum added,
typos corrected, references adde
Supersymmetric Vacua in N=2 Supergravity
We use the embedding tensor formalism to analyse maximally symmetric
backgrounds of N=2 gauged supergravities which have the full N=2 supersymmetry.
We state the condition for N=2 vacua and discuss some of their general
properties. We show that if the gauged isometries leave the SU(2) R-symmetry
invariant, then the N=2 vacuum must be Minkowski. This implies that there are
no AdS backgrounds with eight unbroken supercharges in the effective N=2
supergravity of six-dimensional SU(3) x SU(3) structure compactifications of
type II string theory and M-theory. Combined with previous results on N=1
vacua, we show that there exist N=2 supergravities with a given set of gauged
Abelian isometries that have both N=2 and N=1 vacua. We also argue that an
analogue of our analysis holds in five and six spacetime dimensions.Comment: 14 pages, v2: references added, statement on SU(3) x SU(3) structure
compactifications clarified; v3: published version with statement on moduli
space of N=2 AdS vacua correcte