11,274 research outputs found
Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypes
An answer to the question: Can, in general, the adoption of a given symmetry
induce a further symmetry, which might be hidden at a first level? has been
attempted in the context of differential geometry of locally homogeneous
spaces. Based on E. Cartan's theory of moving frames, a methodology for finding
all symmetries for any n dimensional locally homogeneous space is provided. The
analysis is applied to 3 dimensional spaces, whereby the embedding of them into
a 4 dimensional Lorentzian manifold is examined and special solutions to
Einstein's field equations are recovered. The analysis is mainly of local
character, since the interest is focused on local structures based on
differential equations (and their symmetries), rather than on the implications
of, e.g., the analytic continuation of their solution(s) and their dynamics in
the large.Comment: 27 pages, no figues, no tables, one reference added, spelling and
punctuation issues correcte
Spinorial geometry and Killing spinor equations of 6-D supergravity
We solve the Killing spinor equations of 6-dimensional (1,0)-supergravity
coupled to any number of tensor, vector and scalar multiplets in all cases. The
isotropy groups of Killing spinors are Sp(1)\cdot Sp(1)\ltimes \bH (1),
U(1)\cdot Sp(1)\ltimes \bH (2), Sp(1)\ltimes \bH (3,4), , and , where in parenthesis is the number of supersymmetries
preserved in each case. If the isotropy group is non-compact, the spacetime
admits a parallel null 1-form with respect to a connection with torsion the
3-form field strength of the gravitational multiplet. The associated vector
field is Killing and the 3-form is determined in terms of the geometry of
spacetime. The Sp(1)\ltimes \bH case admits a descendant solution preserving
3 out of 4 supersymmetries due to the hyperini Killing spinor equation. If the
isotropy group is compact, the spacetime admits a natural frame constructed
from 1-form spinor bi-linears. In the and U(1) cases, the spacetime
admits 3 and 4 parallel 1-forms with respect to the connection with torsion,
respectively. The associated vector fields are Killing and under some
additional restrictions the spacetime is a principal bundle with fibre a
Lorentzian Lie group. The conditions imposed by the Killing spinor equations on
all other fields are also determined.Comment: 34 pages, Minor change
The holonomy of IIB supercovariant connection
We show that the holonomy of the supercovariant connection of IIB
supergravity is contained in SL(32, \bR). We also find that the holonomy
reduces to a subgroup of SL(32-N)\st (\oplus^N \bR^{32-N}) for IIB
supergravity backgrounds with Killing spinors. We give the necessary and
sufficient conditions for a IIB background to admit Killing spinors. A IIB
supersymmetric probe configuration can involve up to 31 linearly independent
planar branes and preserves one supersymmetry.Comment: 8 pages, latex. v2: Minor correction
Curved branes from string dualities
We describe a simple method for generating new string solutions for which the
brane worldvolume is a curved space. As a starting point we use solutions with
NS-NS charges combined with 2-d CFT's representing different parts of
space-time. We illustrate our method with many examples, some of which are
associated with conformally invariant sigma models. Using U-duality, we also
obtain supergravity solutions with RR charges which can be interpreted as
D-branes with non-trivial worldvolume geometry. In particular, we discuss the
case of a D5-brane wrapped on AdS_3 x S^3, a solution interpolating between
AdS_3 x S^3 x R^5 and AdS_3 x S^3 x S^3 x R, and a D3-brane wrapped over S^3 x
R or AdS_2 x S^2. Another class of solutions we discuss involves NS5-branes
intersecting over a 3-space and NS5-branes intersecting over a line. These
solutions are similar to D7-brane or cosmic string backgrounds.Comment: 21 pages, harvmac; misprint correcte
Penrose Limits and Spacetime Singularities
We give a covariant characterisation of the Penrose plane wave limit: the
plane wave profile matrix is the restriction of the null geodesic
deviation matrix (curvature tensor) of the original spacetime metric to the
null geodesic, evaluated in a comoving frame. We also consider the Penrose
limits of spacetime singularities and show that for a large class of black
hole, cosmological and null singularities (of Szekeres-Iyer ``power-law
type''), including those of the FRW and Schwarzschild metrics, the result is a
singular homogeneous plane wave with profile , the scale
invariance of the latter reflecting the power-law behaviour of the
singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction
The spinorial geometry of supersymmetric backgrounds
We propose a new method to solve the Killing spinor equations of
eleven-dimensional supergravity based on a description of spinors in terms of
forms and on the Spin(1,10) gauge symmetry of the supercovariant derivative. We
give the canonical form of Killing spinors for N=2 backgrounds provided that
one of the spinors represents the orbit of Spin(1,10) with stability subgroup
SU(5). We directly solve the Killing spinor equations of N=1 and some N=2, N=3
and N=4 backgrounds. In the N=2 case, we investigate backgrounds with SU(5) and
SU(4) invariant Killing spinors and compute the associated spacetime forms. We
find that N=2 backgrounds with SU(5) invariant Killing spinors admit a timelike
Killing vector and that the space transverse to the orbits of this vector field
is a Hermitian manifold with an SU(5)-structure. Furthermore, N=2 backgrounds
with SU(4) invariant Killing spinors admit two Killing vectors, one timelike
and one spacelike. The space transverse to the orbits of the former is an
almost Hermitian manifold with an SU(4)-structure and the latter leaves the
almost complex structure invariant. We explore the canonical form of Killing
spinors for backgrounds with extended, N>2, supersymmetry. We investigate a
class of N=3 and N=4 backgrounds with SU(4) invariant spinors. We find that in
both cases the space transverse to a timelike vector field is a Hermitian
manifold equipped with an SU(4)-structure and admits two holomorphic Killing
vector fields. We also present an application to M-theory Calabi-Yau
compactifications with fluxes to one-dimension.Comment: Latex, 54 pages, v2: clarifications made and references added. v3:
minor changes. v4: minor change
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