12,313 research outputs found
Some Lipschitz maps between hyperbolic surfaces with applications to TeichmĂŒller theory
International audienceIn the TeichmĂŒller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to reparametrization). The lines we construct are special stretch lines in the sense of Thurston. They are directed by complete geodesic laminations that are not chain-recurrent, and they have a nice description in terms of Fenchel-Nielsen coordinates. At the basis of the construction are certain maps with controlled Lipschitz constants between right-angled hyperbolic hexagons having three non-consecutive edges of the same size. Using these maps, we obtain Lipschitz-minimizing maps between hyperbolic particular pairs of pants and, more generally, between some hyperbolic sufaces of finite type with arbitrary genus and arbitrary number of boundary components. The Lipschitz-minimizing maps that we contruct are distinct from Thurston's stretch maps
Grassmannians,Calibrations and Five-Brane Intersections
We present a geometric construction of a new class of hyper-Kahler manifolds
with torsion. This involves the superposition of the four-dimensional
hyper-Kahler geometry with torsion associated with the NS-5-brane along
quaternionic planes in quaternionic k-space, \bH^k. We find the moduli space
of these geometries and show that it can be constructed using the bundle space
of the canonical quaternionic line bundle over a quaternionic projective space.
We also investigate several special cases which are associated with certain
classes of quaternionic planes in \bH^k. We then show that the
eight-dimensional geometries we have found can be constructed using
quaternionic calibrations. We generalize our construction to superpose the same
four-dimensional hyper-Kahler geometry with torsion along complex planes in
\bC^{2k}. We find that the resulting geometry is Kahler with torsion. The
moduli space of these geometries is also investigated. In addition, the
applications of these new geometries to M-theory and sigma models are
presented. In particular, we find new solutions of IIA supergravity with the
interpretation of intersecting NS-5-branes at Sp(2)-angles on a string and show
that they preserve 3/32, 1/8, 5/32 and 3/16 of supersymmetry. We also show that
two-dimensional sigma models with target spaces the above manifolds have (p,q)
extended supersymmetry.Comment: 39 pages, phyzzx; a previously undetermined fraction of supersymmetry
has now been fixed; a table has been replaced; version submitted for
publication in CM
Instantons at Angles
We interpret a class of 4k-dimensional instanton solutions found by Ward,
Corrigan, Goddard and Kent as four-dimensional instantons at angles. The
superposition of each pair of four-dimensional instantons is associated with
four angles which depend on some of the ADHM parameters. All these solutions
are associated with the group and are examples of Hermitian-Einstein
connections on \bE^{4k}. We show that the eight-dimensional solutions
preserve 3/16 of the ten-dimensional N=1 supersymmetry. We argue that under the
correspondence between the BPS states of Yang-Mills theory and those of
M-theory that arises in the context of Matrix models, the instantons at angles
configuration corresponds to the longitudinal intersecting 5-branes on a string
at angles configuration of M-theory.Comment: 17 pages, phyzzx, many changes and a new section was adde
A hierarchical phase space generator for QCD antenna structures
We present a ``hierarchical'' strategy for phase space generation in order to
efficiently map the antenna momentum structures, typically occurring in QCD
amplitudes.Comment: 21 pages, few typos corrected, figure added, to appear in
Eur.Phys.J.
Solitons in (1,1)-supersymmetric massive sigma model
We find the solitons of massive (1,1)-supersymmetric sigma models with target
space the groups and for a class of scalar potentials and
compute their charge, mass and moduli space metric. We also investigate the
massive sigma models with target space any semisimple Lie group and show that
some of their solitons can be obtained from embedding the and
solitons.Comment: Phyzzx.tex, 32 pp, 3 fig
AdS4 backgrounds with N>16 supersymmetries in 10 and 11 dimensions
We explore all warped backgrounds with the most
general allowed fluxes that preserve more than 16 supersymmetries in -
and -dimensional supergravities. After imposing the assumption that either
the internal space is compact without boundary or the isometry
algebra of the background decomposes into that of AdS and that of
, we find that there are no such backgrounds in IIB supergravity.
Similarly in IIA supergravity, there is a unique such background with 24
supersymmetries locally isometric to , and in
supergravity all such backgrounds are locally isometric to the maximally
supersymmetric solution.Comment: 53 pages. v2: minor changes and references added. v3: typos corrected
and minor footnote added, published versio
Twistor Spaces for QKT Manifolds
We find that the target space of two-dimensional (4,0) supersymmetric sigma
models with torsion coupled to (4,0) supergravity is a QKT manifold, that is, a
quaternionic K\"ahler manifold with torsion. We give four examples of
geodesically complete QKT manifolds one of which is a generalisation of the
LeBrun geometry. We then construct the twistor space associated with a QKT
manifold and show that under certain conditions it is a K\"ahler manifold with
a complex contact structure. We also show that, for every 4k-dimensional QKT
manifold, there is an associated 4(k+1)-dimensional hyper-K\"ahler one.Comment: 25 pages, phyzz
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