Calibrations and Fayyazuddin-Smith spacetimes

We study the geometry of M5-branes wrapping a 2-cycle which is Special Lagrangian with respect to a specific complex structure in a CalabiYau 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 nonintegrable almost complex structure and a (2,0) form. This time, however, due to the hyper-Kähler 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. HUTP-05/A0040BCCUNY-HEP /05-04 hep-th/xxxxxxx *

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“…which is in the form advocated in [4]. We have thus completely recovered the results of [2] and [4].…”

Section: Transforming Special Lagrangians To Holomorphic Cyclessupporting

confidence: 59%

“…In addition we have proven the correctness of the key assumption of these works: that there is a complex structure. In [2] and [4] no use was made of the (2,0) form. Our analysis in this paper suggests that the (2,0) form is a well-defined object in the theory which satisfies the identity (30).…”

Section: Transforming Special Lagrangians To Holomorphic Cyclesmentioning

confidence: 99%

Geometry of wrapped M5-branes in Calabi-Yau 2-folds

2006

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“…We consider background geometries of M5-and M2-branes wrapping different cycles of CalabiYau manifolds. We will introduce all possible supersymmetric probes and derive constraints on the background geometry from requiring that the mass calibrating form (8) d 0 for the probe is closed. In what follows we use the convention that for wrapped M5 backgrounds H 2 1 H ÿ1=3 and for wrapped M2-branes H 2 1 H ÿ2=3 .…”

Section: Torsion Classes From Calibrationsmentioning

confidence: 99%

Calibrations, torsion classes, and wrapped M-branes

Fayyazuddin

Husain

2006

Phys. Rev. D

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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 manifold. 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.

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“…The supersymmetry conditions for a single timelike Killing spinor in eleven dimensions (as appropriate for the description of M5 branes on SLAG five-cycles) were first given in [13]. Membranes wrapping holomorphic curves in Calabi-Yau manifolds were studied, using the Fayyazuddin-Smith ansatz and from the perspective of generalised calibrations, in [33] and [45]. The conditions for minimally supersymmetric AdS 2 spacetimes in M-theory, with vanishing magnetic flux and compact internal space, were derived in [43].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric wrapped membranes,AdS₂spaces, and bubbling geometries

Conamhna

Colgáin

2007

J. High Energy Phys.

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We perform a systematic study, in eleven dimensional supergravity, of the geometry of wrapped brane configurations admitting AdS 2 limits. Membranes wrapping holomorphic curves in Calabi-Yau manifolds are found to exhibit some novel features; in particular, for fourfolds or threefolds, the gravitational effect of the branes on the overall transverse space is only weakly restricted by the kinematics of the Killing spinor equation. We also study the AdS 2 limits of the wrapped brane supergravity descriptions. From the description of membranes wrapped in a two-fold, we derive a set of AdS 2 supersymmetry conditions which upon analytic continuation coincide precisely with those for the half-BPS bubbling geometries of LLM. From the near-horizon limit of membranes wrapped in a three-fold, we obtain a set of supersymmetry conditions which upon analytic continuation describe a class of spacetimes which we identify as quarter-BPS bubbling geometries in Mtheory, with SO(4) × SO(3) × U(1) isometry in Riemannian signature. We also study fivebranes wrapping a special lagrangian five-cycle in a fivefold, in the presence of membranes wrapping holomorphic curves, and employ the wrapped brane supersymmetry conditions to derive a classification of the general minimally supersymmetric AdS 2 geometry in M-theory.

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Calibrations and Fayyazuddin-Smith spacetimes

Cited by 27 publications

References 34 publications

Geometry of wrapped M5-branes in Calabi-Yau 2-folds

Geometry of wrapped M5-branes in Calabi-Yau 2-folds

Calibrations, torsion classes, and wrapped M-branes

Supersymmetric wrapped membranes,AdS₂spaces, and bubbling geometries

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Calibrations and Fayyazuddin-Smith spacetimes

Cited by 27 publications

References 34 publications

Geometry of wrapped M5-branes in Calabi-Yau 2-folds

Geometry of wrapped M5-branes in Calabi-Yau 2-folds

Calibrations, torsion classes, and wrapped M-branes

Supersymmetric wrapped membranes,AdS2spaces, and bubbling geometries

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Supersymmetric wrapped membranes,AdS₂spaces, and bubbling geometries