G-Structures, Fluxes and Calibrations in M-Theory

TL;DR

This paper characterizes supersymmetric warped M-theory backgrounds with fluxes using G-structures, deriving conditions for supersymmetry preservation and exploring calibrated M-brane configurations in special geometric settings.

Contribution

It provides necessary and sufficient G-structure-based conditions for supersymmetry in warped M-theory backgrounds with fluxes, including new explicit M-brane solutions.

Findings

Derived supersymmetry conditions in terms of G-structures and intrinsic torsion.

Formulated calibration conditions for dyonic M-branes with fluxes.

Constructed new explicit examples of supersymmetric M-brane configurations.

Abstract

We study the most general supersymmetric warped M-theory backgrounds with non-trivial G-flux of the type R^{1,2} x M_8 and AdS_3 x 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 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 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.