609 research outputs found

### Supersymmetric Intersecting D6-Branes and Fluxes in Massive Type IIA String Theory

We study N=1 supersymmetric four-dimensional solutions of massive Type IIA supergravity with intersecting D6-branes in the presence NS-NS three-form fluxes. We derive N=1 supersymmetry conditions for the D6-brane and flux configurations in an internal manifold X6 and derive the intrinsic torsion (or SU(3)-structure) related to the fluxes. In the absence of fluxes, N=1 supersymmetry implies that D6-branes wrap supersymmetric three-cycles of X6 that intersect at angles of SU(3) rotations and the geometry is deformed by SU(3)-structures. The presence of fluxes breaks the SU(3) structures to SU(2) and the D6-branes intersect at angles of SU(2) rotations; non-zero mass parameter corresponds to D8-branes which are orthogonal to the common cycle of all D6-branes. The anomaly inflow indicates that the gauge theory on intersecting (massive) D6-branes is not chiral

### Bent BPS domain walls of D=5 N=2 gauged supergravity coupled to hypermultiplets

Within D=5 N=2 gauged supergravity coupled to hypermultiplets we derive
consistency conditions for BPS domain walls with constant negative curvature on
the wall. For such wall solutions to exist, the covariant derivative of the
projector, governing the constraint on the Killing spinor, has to be non-zero
and proportional to the cosmological constant on the domain walls. We also
prove that in this case solutions of the Killing spinor equations are solutions
of the equations of motion. We present explicit, analytically solved examples
of such domain walls, employing the universal hypermultiplet fields. These
examples involve the running of two scalar fields and the space-time in the
transverse direction that is cut off at a critical distance, governed by the
magnitude of the negative cosmological constant on the wall.Comment: 18 pages, Late

### Scattering Theory for Open Quantum Systems

Quantum systems which interact with their environment are often modeled by
maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper
the scattering theory for such open systems is considered. First it is assumed
that a single maximal dissipative operator $A_D$ in a Hilbert space \sH is
used to describe an open quantum system. In this case the minimal self-adjoint
dilation $\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed
system which contains the open system \{A_D,\sH\}, but since $\widetilde K$
is necessarily not semibounded from below, this model is difficult to interpret
from a physical point of view. In the second part of the paper an open quantum
system is modeled with a family $\{A(\mu)\}$ of maximal dissipative operators
depending on energy $\mu$, and it is shown that the open system can be embedded
into a closed system where the Hamiltonian is semibounded. Surprisingly it
turns out that the corresponding scattering matrix can be completely recovered
from scattering matrices of single Pseudo-Hamiltonians as in the first part of
the paper. The general results are applied to a class of Sturm-Liouville
operators arising in dissipative and quantum transmitting
Schr\"{o}dinger-Poisson systems

### Dirichlet-to-Neumann maps on bounded Lipschitz domains

The Dirichlet-to-Neumann map associated to an elliptic partial differential
equation becomes multivalued when the underlying Dirichlet problem is not
uniquely solvable. The main objective of this paper is to present a systematic
study of the Dirichlet-to-Neumann map and its inverse, the Neumann-to-Dirichlet
map, in the framework of linear relations in Hilbert spaces. Our treatment is
inspired by abstract methods from extension theory of symmetric operators,
utilizes the general theory of linear relations and makes use of some deep
results on the regularity of the solutions of boundary value problems on
bounded Lipschitz domains

### Scattering matrices and Weyl functions

For a scattering system $\{A_\Theta,A_0\}$ consisting of selfadjoint
extensions $A_\Theta$ and $A_0$ of a symmetric operator $A$ with finite
deficiency indices, the scattering matrix \{S_\gT(\gl)\} and a spectral shift
function $\xi_\Theta$ are calculated in terms of the Weyl function associated
with the boundary triplet for $A^*$ and a simple proof of the Krein-Birman
formula is given. The results are applied to singular Sturm-Liouville operators
with scalar and matrix potentials, to Dirac operators and to Schr\"odinger
operators with point interactions.Comment: 39 page

### Trace formulae for dissipative and coupled scattering systems

For scattering systems consisting of a (family of) maximal dissipative
extension(s) and a selfadjoint extension of a symmetric operator with finite
deficiency indices, the spectral shift function is expressed in terms of an
abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is
proved.Comment: 38 page

### Domain Wall World(s)

Gravitational properties of domain walls in fundamental theory and their
implications for the trapping of gravity are reviewed. In particular, the
difficulties to embed gravity trapping configurations within gauged
supergravity is reviewed and the status of the domain walls obtained via the
breathing mode of sphere reduced Type IIB supergravity is presented.Comment: 11 pages, Based on talk given at Strings 2000 Minor corrections,
references adde

### 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

### Time-dependent backgrounds from supergravity with gauged non-compact R-symmetry

We obtain a general class of time-dependent, asymptotically de Sitter
backgrounds which solve the first order bosonic equations that extremize the
action for supergravity with gauged non-compact $R$-symmetry. These backgrounds
correspond only to neutral fields with the correct sign of kinetic energy.
Within N=2 five-dimensional supergravity with vector-superfields we provide
examples of multi-centered charged black holes in asymptotic de Sitter space,
whose spatial part is given by a time-dependent hyper-K\"ahler space. Reducing
these backgrounds to four dimensions yields asymptotically de Sitter
multi-centered charged black hole backgrounds and we show that they are related
to an instanton configuration by a massive T-duality over time. Within N=2
gauged supergravity in four (and five)-dimensions with hyper-multiplets there
could also be neutral cosmological backgrounds that are regular and correspond
to the different de Sitter spaces at early and late times.Comment: 28 pages, Latex; minor changes and add reference

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