8,395 research outputs found
Gravity duals of supersymmetric gauge theories on three-manifolds
We study gravity duals to a broad class of N=2 supersymmetric gauge theories
defined on a general class of three-manifold geometries. The gravity
backgrounds are based on Euclidean self-dual solutions to four-dimensional
gauged supergravity. As well as constructing new examples, we prove in general
that for solutions defined on the four-ball the gravitational free energy
depends only on the supersymmetric Killing vector, finding a simple closed
formula when the solution has U(1) x U(1) symmetry. Our result agrees with the
large N limit of the free energy of the dual gauge theory, computed using
localization. This constitutes an exact check of the gauge/gravity
correspondence for a very broad class of gauge theories with a large N limit,
defined on a general class of background three-manifold geometries.Comment: 74 pages, 2 figures; v2: minor change
Holographic renormalization and supersymmetry
Holographic renormalization is a systematic procedure for regulating
divergences in observables in asymptotically locally AdS spacetimes. For dual
boundary field theories which are supersymmetric it is natural to ask whether
this defines a supersymmetric renormalization scheme. Recent results in
localization have brought this question into sharp focus: rigid supersymmetry
on a curved boundary requires specific geometric structures, and general
arguments imply that BPS observables, such as the partition function, are
invariant under certain deformations of these structures. One can then ask if
the dual holographic observables are similarly invariant. We study this
question in minimal N = 2 gauged supergravity in four and five dimensions. In
four dimensions we show that holographic renormalization precisely reproduces
the expected field theory results. In five dimensions we find that no choice of
standard holographic counterterms is compatible with supersymmetry, which leads
us to introduce novel finite boundary terms. For a class of solutions
satisfying certain topological assumptions we provide some independent tests of
these new boundary terms, in particular showing that they reproduce the
expected VEVs of conserved charges.Comment: 70 pages; corrected typo
The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six dimensions
We obtain necessary and sufficient conditions for a supersymmetric field
configuration in the N=(1,0) U(1) or SU(2) gauged supergravities in six
dimensions, and impose the field equations on this general ansatz. It is found
that any supersymmetric solution is associated to an structure. The structure is characterized by a null Killing
vector which induces a natural 2+4 split of the six dimensional spacetime. A
suitable combination of the field equations implies that the scalar curvature
of the four dimensional Riemannian part, referred to as the base, obeys a
second order differential equation. Bosonic fluxes introduce torsion terms that
deform the structure away from a covariantly
constant one. The most general structure can be classified in terms of its
intrinsic torsion. For a large class of solutions the gauge field strengths
admit a simple geometrical interpretation: in the U(1) theory the base is
K\"{a}hler, and the gauge field strength is the Ricci form; in the SU(2)
theory, the gauge field strengths are identified with the curvatures of the
left hand spin bundle of the base. We employ our general ansatz to construct
new supersymmetric solutions; we show that the U(1) theory admits a symmetric
Cahen-Wallach solution together with a compactifying pp-wave. The
SU(2) theory admits a black string, whose near horizon limit is . We also obtain the Yang-Mills analogue of the Salam-Sezgin solution of
the U(1) theory, namely , where the is supported by a
sphaleron. Finally we obtain the additional constraints implied by enhanced
supersymmetry, and discuss Penrose limits in the theories.Comment: 1+29 pages, late
M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds
Seven-dimensional inhomogeneous Sasaki-Einstein manifolds
present a challenging example of AdS/CFT correspondence. At present, their
field theory duals for base are proposed only within a
restricted range as quiver Chern-Simons-matter
theories with gauge group, nine bifundamental
chiral multiplets interacting through a cubic superpotential. To further
elucidate this correspondence, we use particle approximation both at classical
and quantum level. We setup a concrete AdS/CFT mapping of conserved quantities
using geodesic motions, and turn to solutions of scalar Laplace equation in
. The eigenmodes also provide an interesting subset of Kaluza-Klein
spectrum for supergravity in , and are dual
to protected operators written in terms of matter multiplets in the dual
conformal field theory.Comment: v2 refs added. 19 pages 1 figur
On the Ricci tensor in type II B string theory
Let be a metric connection with totally skew-symmetric torsion \T
on a Riemannian manifold. Given a spinor field and a dilaton function
, the basic equations in type II B string theory are \bdm \nabla \Psi =
0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi
= b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations
between the length ||\T||^2 of the torsion form, the scalar curvature of
, the dilaton function and the parameters . The main
results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the
connection. In particular, if the supersymmetry is non-trivial and if
the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d
\T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is
divergence-free. We show that the latter condition is satisfied in many
examples constructed out of special geometries. A special case is . Then
the divergence of the energy-momentum tensor vanishes if and only if one
condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T =
0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq
0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2
Randomizing world trade. II. A weighted network analysis
Based on the misleading expectation that weighted network properties always
offer a more complete description than purely topological ones, current
economic models of the International Trade Network (ITN) generally aim at
explaining local weighted properties, not local binary ones. Here we complement
our analysis of the binary projections of the ITN by considering its weighted
representations. We show that, unlike the binary case, all possible weighted
representations of the ITN (directed/undirected, aggregated/disaggregated)
cannot be traced back to local country-specific properties, which are therefore
of limited informativeness. Our two papers show that traditional macroeconomic
approaches systematically fail to capture the key properties of the ITN. In the
binary case, they do not focus on the degree sequence and hence cannot
characterize or replicate higher-order properties. In the weighted case, they
generally focus on the strength sequence, but the knowledge of the latter is
not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243
[physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011
All supersymmetric solutions of minimal supergravity in six dimensions
A general form for all supersymmetric solutions of minimal supergravity in
six dimensions is obtained. Examples of new supersymmetric solutions are
presented. It is proven that the only maximally supersymmetric solutions are
flat space, AdS_3 x S^3 and a plane wave. As an application of the general
solution, it is shown that any supersymmetric solution with a compact horizon
must have near-horizon geometry R^{1,1} x T^4, R^{1,1} x K3 or identified AdS_3
x S^3.Comment: 40 pages. v2: two references adde
New Results in Sasaki-Einstein Geometry
This article is a summary of some of the author's work on Sasaki-Einstein
geometry. A rather general conjecture in string theory known as the AdS/CFT
correspondence relates Sasaki-Einstein geometry, in low dimensions, to
superconformal field theory; properties of the latter are therefore reflected
in the former, and vice versa. Despite this physical motivation, many recent
results are of independent geometrical interest, and are described here in
purely mathematical terms: explicit constructions of infinite families of both
quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry;
an extremal problem that determines the Reeb vector field for, and hence also
the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the
existence of Sasaki-Einstein metrics. Some of these results also provide new
insights into Kahler geometry, and in particular new obstructions to the
existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the
conference "Riemannian Topology: Geometric Structures on Manifolds"; minor
typos corrected, reference added; published version; Riemannian Topology and
Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov
2008
Symplectic potentials and resolved Ricci-flat ACG metrics
We pursue the symplectic description of toric Kahler manifolds. There exists
a general local classification of metrics on toric Kahler manifolds equipped
with Hamiltonian two-forms due to Apostolov, Calderbank and Gauduchon(ACG). We
derive the symplectic potential for these metrics. Using a method due to Abreu,
we relate the symplectic potential to the canonical potential written by
Guillemin. This enables us to recover the moment polytope associated with
metrics and we thus obtain global information about the metric. We illustrate
these general considerations by focusing on six-dimensional Ricci flat metrics
and obtain Ricci flat metrics associated with real cones over L^{pqr} and
Y^{pq} manifolds. The metrics associated with cones over Y^{pq} manifolds turn
out to be partially resolved with two blowup parameters taking special
(non-zero)values. For a fixed Y^{pq} manifold, we find explicit metrics for
several inequivalent blow-ups parametrised by a natural number k in the range
0<k<p. We also show that all known examples of resolved metrics such as the
resolved conifold and the resolution of C^3/Z_3 also fit the ACG
classification.Comment: LaTeX, 34 pages, 4 figures (v2)presentation improved, typos corrected
and references added (v3)matches published versio
GaAs:Mn nanowires grown by molecular beam epitaxy of (Ga,Mn)As at MnAs segregation conditions
GaAs:Mn nanowires were obtained on GaAs(001) and GaAs(111)B substrates by
molecular beam epitaxial growth of (Ga,Mn)As at conditions leading to MnAs
phase separation. Their density is proportional to the density of catalyzing
MnAs nanoislands, which can be controlled by the Mn flux and/or the substrate
temperature. Being rooted in the ferromagnetic semiconductor (Ga,Mn)As, the
nanowires combine one-dimensional properties with the magnetic properties of
(Ga,Mn)As and provide natural, self assembled structures for nanospintronics.Comment: 13 pages, 6 figure
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