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G structures, fluxes, and calibrations in M theory

2003; American Physical Society; Volume: 68; Issue: 8 Linguagem: Inglês

10.1103/physrevd.68.085014

1538-4500

Dario Martelli, James Sparks,

Galaxies: Formation, Evolution, Phenomena

We study the most general supersymmetric warped M-theory backgrounds with a non-trivial G flux of the type ${R}^{1,2}\ifmmode\times\else\texttimes\fi{}{\mathrm{M}}_{8}$ and ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{M}}_{8}.$ We give a set of necessary and sufficient conditions for preservation of supersymmetry which are phrased in terms of G structures and their intrinsic torsion. These equations may be interpreted as calibration conditions for a static ``dyonic'' M-brane, that is, an M5-brane with a self-dual three-form turned on. When the electric flux is turned off we obtain the supersymmetry conditions and non-linear PDEs describing M5-branes wrapped on associative and special Lagrangian three-cycles in manifolds with ${G}_{2}$ and $\mathrm{SU}(3)$ structures, respectively. As an illustration of our formalism, we recover the 1/2 BPS dyonic M-brane, and also construct some new examples.