105 research outputs found

### A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator
are studied under the assumption that the weight function has one turning
point. An abstract approach to the problem is given via a functional model for
indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues
are obtained. Also, operators with finite singular critical points are
considered.Comment: 38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4,
and 3.12 extended, details added in subsections 2.3 and 4.2, section 6
rearranged, typos corrected, references adde

### Classification of Supersymmetric Flux Vacua in M Theory

We present a comprehensive classification of supersymmetric vacua of M-theory
compactification on seven-dimensional manifolds with general four-form fluxes.
We analyze the cases where the resulting four-dimensional vacua have N =
1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2
structures. In particular, we find for N = 2 supersymmetry, that the external
space-time is Minkowski and the base manifold of the internal space is
conformally K\"ahler for SU(2) structures, while for SU(3) structures the
internal space has to be Einstein-Sasaki and no internal fluxes are allowed.
Moreover, we provide a new vacuum with N = 1 supersymmetry and SU(3) structure,
where all fluxes are non-zero and the first order differential equations are
solved.Comment: 50 pages, clarification of the spinor ansatz added, references added,
typos correcte

### Exploring the relation between 4D and 5D BPS solutions

Based on recent proposals linking four and five-dimensional BPS solutions, we
discuss the explicit dictionary between general stationary 4D and 5D
supersymmetric solutions in N=2 supergravity theories with cubic prepotentials.
All these solutions are completely determined in terms of the same set of
harmonic functions and the same set of attractor equations. As an example, we
discuss black holes and black rings in G\"odel-Taub-NUT spacetime. Then we
consider corrections to the 4D solutions associated with more general
prepotentials and comment on analogous corrections on the 5D side.Comment: 33 pages; refs adde

### General N = 1 Supersymmetric Fluxes in Massive Type IIA String Theory

We study conditions on general fluxes of massive Type IIA supergravity that
lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these
conditions in the case of SU(3)- as well as SU(2)-structures. SU(3)-structures
imply that the internal space is constrained to be a nearly K\"ahler manifold
with all the turned on fluxes, and the negative cosmological constant
proportional to the mass parameter, and the dilaton fixed by the quantized
ratio of the three-form and four-form fluxes. We further discuss the
implications of such flux vacua with added intersecting D6-branes, leading to
the chiral non-Abelian gauge sectors (without orientifold projections).
Examples that break SU(3)-structures to SU(2)-ones allow for the internal space
conformally flat (up to orbifold and orientifold projections), for which we
give an explicit example. These results provide a starting point for further
study of the four-dimensional (chiral) N = 1 supersymmetric solutions of
massive Type IIA supergravity with D-branes and fluxes, compactified on
orientifolds.Comment: 37 pages; changed the resulting gauge group on intersecting 6-branes,
corrected the explicit example (with conformal flat internal space) as well
as minor modifications and add a re

### General N = 1 Supersymmetric Flux Vacua of (Massive) Type IIA String Theory

We derive conditions for the existence of four-dimensional \N=1
supersymmetric flux vacua of massive type IIA string theory with general
supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show
that such flux vacua exist only when the internal geometry is nearly-K\"ahler.
The geometry is not warped, all the allowed fluxes are proportional to the mass
parameter and the dilaton is fixed by a ratio of (quantized) fluxes. The
four-dimensional cosmological constant, while negative, becomes small in the
vacuum with the weak string coupling.Comment: 4 page

### Fluxes in M-theory on 7-manifolds: G_2-, SU(3)- and SU(2)-structures

We consider compactifications of M-theory on 7-manifolds in the presence of
4-form fluxes, which leave at least four supercharges unbroken. Supersymmetric
vacua admit G-structures and we discuss the cases of G_2-, SU(3)- as well as
SU(2)-structures. We derive the constraints on the fluxes imposed by
supersymmetry and determine the flux components that fix the resulting
4-dimensional cosmological constant (i.e. superpotential).Comment: 17 pages, contribution for the proceedings of: BW2003 Workshop, 29
Aug. - 02 Sept., 2003 Vrnjacka Banja, Serbi

### Black holes in Goedel-type universes with a cosmological constant

We discuss supersymmetric black holes embedded in a Goedel-type universe with
cosmological constant in five dimensions. The spacetime is a fibration over a
four-dimensional Kaehler base manifold, and generically has closed timelike
curves. Asymptotically the space approaches a deformation of AdS_5, which
suggests that the appearance of closed timelike curves should have an
interpretation in some deformation of D=4, N=4 super-Yang-Mills theory.
Finally, a Goedel-de Sitter universe is also presented and its causal structure
is discussed.Comment: 25 pages, Latex, no figures, references updated, physical discussion
of the solutions considerably expanded, holographic stress tensor and
conserved charges of Goedel-AdS(5) solution compute

### Superpotentials from flux compactifications of M-theory

In flux compactifications of M-theory a superpotential is generated whose
explicit form depends on the structure group of the 7-dimensional internal
manifold. In this note, we discuss superpotentials for the structure groups:
G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For
SU(3) structures, the non-zero flux components entering the superpotential
describe an effective 1-dimensional model and a Chern-Simons model if there are
SU(2) structures.Comment: 10 page

### Intersecting branes from 7-manifolds with G_2 holonomy

In this talk I discuss intersecting brane configurations coming from explicit
metrics with G_2 holonomy. An example of a 7-manifold which representing a R^3
bundle over a self-dual Einstein space is described and the potential appearing
after compactification over the 6-d twistor space is derived.Comment: 7 pages, Latex, talk presented at the 35th Symposium Ahrenshoop,
August 200

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