Calibrations, torsion classes, and wrapped M-branes

Fayyazuddin, Ansar; Husain, Tasneem Zehra

doi:10.1103/physrevd.73.106007

Cited by 8 publications

(33 citation statements)

References 12 publications

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“…We will find that, just as in [6], we get constraints on J and Ω giving us important information about the manifold M.…”

Section: Probing a D6-brane On A Spell3-cyclementioning

confidence: 99%

“…As argued in [6] the tension for a supersymmetric probe brane is given by a calibrating form integrated over the cycle the brane is wrapping. In this case the D2-brane is wrapping a 0-cycle and therefore the tension is given by a calibrated form only if…”

Section: D-brane Probesmentioning

confidence: 99%

“…Such branes, being BPS, are not only stable but also static. We compute their mass (or tension) and associate it with a calibrating form integrated over the cycle wrapped by the probe [6]. In what follows, we use this method to identify the calibrating forms in the supergravity background generated by D6-branes wrapping a Special Lagrangian 3-cycle.…”

Section: How Brane Probes Help Characterize a Backgroundmentioning

confidence: 99%

“…In what follows, we use this method to identify the calibrating forms in the supergravity background generated by D6-branes wrapping a Special Lagrangian 3-cycle. The properties of these calibrating forms give the torsion class constraints [6] and thereby allows us to characterize the background.…”

Section: How Brane Probes Help Characterize a Backgroundmentioning

confidence: 99%

“…We will apply a recently introduced technique [6] to classify the backgrounds created by wrapped branes. As we illustrate in the present work, this method provides us with an efficient way of finding the torsion class constraints on the geometry.…”

Section: Introductionmentioning

confidence: 99%

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G2holonomy metrics and wrapped D6-branes

Fayyazuddin

Husain

2007

Phys. Rev. D

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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 G 2 -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 G 2 -holonomy manifold.

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“…We will find that, just as in [6], we get constraints on J and Ω giving us important information about the manifold M.…”

Section: Probing a D6-brane On A Spell3-cyclementioning

confidence: 99%

Section: D-brane Probesmentioning

confidence: 99%

Section: How Brane Probes Help Characterize a Backgroundmentioning

confidence: 99%

Section: How Brane Probes Help Characterize a Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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G2holonomy metrics and wrapped D6-branes

Fayyazuddin

Husain

2007

Phys. Rev. D

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Calabi–Yau 3-folds from 2-folds

Fayyazuddin¹

2007

Class. Quantum Grav.

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We consider type IIA string theory on a Calabi-Yau 2-fold with D6branes wrapping 2-cycles in the 2-fold. We find a complete set of conditions on the supergravity solution for any given wrapped brane configuration in terms of SU(2) structures. We reduce the problem of finding a supergravity solution for the wrapped branes to finding a harmonic function on R×CY 2 . We then lift this solution to 11-dimensions as a product of R (4.1) and a Calabi-Yau 3-fold. We show how the metric on the 3-fold is determined in terms of the wrapped brane solution. We write down the distinguished (3,0) form and the Kähler form of the 3-fold in terms of structures defined on the base 2-d complex manifold. We discuss the topology of the 3-fold in terms of the D6-branes and the underlying 2fold. We show that in addition to the non-trivial cycles inherited from the underlying 2-fold there are N − 1 new 2-cycles. We construct closed (1,1) forms corresponding to these new cycles. We also display some explicit examples. One of our examples is that of D6-branes wrapping the 2-cycle in an A 1 ALE space, the resulting 3-fold has h (1,1) = N , where N is the number of D6-branes. BCCUNY-HEP /07-01hep-th/0702135 *

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Central charges of wrapped M5-brane backgrounds

Loureda

Smith

2006

J. High Energy Phys.

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We study the central charges of the supersymmetry algebra of branes in backgrounds corresponding to wrapped M5-branes. In the case of M5-branes wrapping a holomorphic 2-cycle in C 2 , we find this allows for a supersymmetric M5-brane probe which is related to the M2-brane probe which describes the BPS spectra of the corresponding N = 2 worldvolume gauge theory. For the case of M5-branes wrapping a holomorphic 2-cycle in C 3 , we find that the central charges allow for a supersymmetric M5-brane probe wrapping a Cayley calibrated 4-cycle, which has an intersecting BPS domain wall interpretation in the corresponding N = 1 MQCD gauge theory. The domain wall is constructed explicitly as an M5-brane wrapping an associative 3-cycle. The tension is found to be the integral of a calibrating form. These wrapped M5-brane backgrounds provide a clear and interesting geometrical realisation of structure groups of M-theory vacua with fluxes.

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Calibrations, torsion classes, and wrapped M-branes

Cited by 8 publications

References 12 publications

G2holonomy metrics and wrapped D6-branes

G2holonomy metrics and wrapped D6-branes

Calabi–Yau 3-folds from 2-folds

Central charges of wrapped M5-brane backgrounds

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