30 research outputs found
holonomy metrics and wrapped D6-branes
We determine torsion class constraints for the supergravity background
produced by D6-branes wrapping special Lagrangian cycles in a Calabi-Yau
3-fold. We employ a recently introduced method which involves probing the
putative background by all possible supersymmetric brane configurations. We
then lift this background to 11-dimensions to a product of 4-d Minkowski space
and a 7-fold of G2-holonomy. The latter is a particular U(1) bundle over an
almost complex manifold of SU(3) structure with specific torsion class
constraints. We construct the closed 3- and 4-forms which calibrate the 3- and
4-cycles in the G2-holonomy manifold.Comment: 21 pages, references adde
The Geometry of M-Branes Wrapping Special Lagrangian Cycles
We characterize the geometry produced by M5-branes wrapping a Special
Lagrangian 3-cycle in a Calabi-Yau 3-fold. The presence of the brane replaces
the the Calabi-Yau by a real manifold with an almost complex structure. We show
that, in this classification, a distinguished (1,1) form as well as a globally
defined (3,0) form play an important role. The requirements of supersymmetry
preservation impose constraints on these structures which can be used to
classify the background.Comment: 17 pages, correct versio
Calibrations, Torsion Classes and Wrapped M-Branes
The present work has two goals. The first is to complete the classification
of geometries in terms of torsion classes of M-branes wrapping cycles of a
Calabi-Yau. The second goal is to give insight into the physical meaning of the
torsion class constraints. We accomplish both tasks by defining new energy
minimizing calibrations in M-brane backgrounds. When fluxes are turned on, it
is these calibrations that are relevant, rather than those which had previously
been defined in the context of purely geometric backgrounds
The geometry of wrapped M5-branes in Calabi-Yau 2-folds
We study the geometry of M5-branes wrapping a 2-cycle which is Special
Lagrangian with respect to a specific complex structure in a Calabi-Yau
two-fold. Using methods recently applied to the three-fold case, we are again
able find a characterization of the geometry, in terms of a non-integrable
almost complex structure and a (2,0) form. This time, however, due to the
hyper-K{\"a}hler nature of the underlying 2-fold we also have the freedom of
choosing a different almost complex structure with respect to which the wrapped
2-cycle is holomorphic. We show that this latter almost complex structure is
integrable. We then relate our geometry to previously found geometries of
M5-branes wrapping holomophic cycles and go further to prove some previously
unknown results for M5-branes on holomorphic cycles
One dimensional M5-brane intersections
We study one dimensional intersections of M5 branes with M5 and M2 branes. On
the worldvolume of the M5-brane, such an intersection appears as a string
soliton. We study this worldvolume theory in two different regimes: 1) Where
the worldvolume theory is formulated in flat space and 2) where the worldvolume
theory is studied in the supergravity background produced by a stack of M5 (or
M2) branes. In both cases, we study the corresponding string solitons, and find
the most general BPS configuration consistent with the fraction of
supersymmetries preserved. We argue that M5 and M2 brane intersections leave
different imprints on the worldvolume theory of the intersecting probe brane,
although geometrically they appear to be similar.Comment: 13 pages, LaTeX, references adde
That's a wrap!
Calibration technology provides us with a fast and elegant way to find the
supergravity solutions for BPS wrapped M-branes. Its true potential had however
remained untapped due to the absence of a classification of calibrations in
spacetimes with non-trivial flux. The applications of this method were thus
limited in practise to M-branes wrapping Kahler calibrated cycles. In this
paper, we catagorize a type of generalised calibrations which exist in
supergravity backgrounds and contain Kahler calibrations as a sub-class. This
broadens the arena of brane configurations whose supergravity solutions are
accessible through the calibration 'short-cut' method.Comment: 19 pages, typos correcte
A Brane Teaser
In this note we study the puzzle posed by two M5-branes intersecting on a
string (or equivalently, a single M5-brane wrapping a holomorphic four-cycle in
C^4). It has been known for a while that this system is different from all
other configurations built using self-intersecting M-branes; in particular the
corresponding supergravity solution exhibits various curious features which
have remained unexplained. We propose that the resolution to these puzzles lies
in the existence of a non-zero two-form on the M5-brane world-volume.Comment: 21 pages. References adde
M2-branes wrapped on holomorphic curves
The generalised calibration for a wrapped membrane is gauge equivalent to the
supergravity three-form under which the membrane is electrically charged. Given
the relevant calibration, one can go a long way towards constructing the
supergravity solution for the wrapped brane. Applications of this method have
been restricted since generalised calibrations have not yet been completely
classified in spacetimes with non-vanishing flux. In this paper, we take a
first step towards such a classification by studying membranes wrapping
holomorphic curves. Supersymmetry preservation imposes a constraint on the
Hermitean metric in the embedding space and it is found that this can be
expressed as a restriction on possible generalised calibrations. Allowed
calibrations in a particular spacetime are simply those which satisfy the
constraint equation relevant to that background; in particular, we see that the
previously considered Kahler calibrations are just a subclass of possible
solutions.Comment: Discussion clarified, typos corrected, references updated. Results
remain unchanged. 12 page