Refining G-structure classifications

Details Refining G-structure classifications Refining G-structure classifications

2004-08-26

arxiv.org/abs/hep-th/0408203v1

Phys.Rev. D70 (2004) 105024

Physics

High Energy Physics

High Energy Physics - Theory

1+45 pages, latex

Scientific paper

10.1103/PhysRevD.70.105024

Using G-structure language, a systematic, iterative formalism for computing neccessary and sufficient conditions for the existence of N arbitrary linearly independent Killing spinors is presented. The key organisational tool is the common isotropy group of the Killing spinors. The formalism is illustrated for configurations in gauged SU(2) supergravity in seven dimensions admitting at least one null Killing spinor, and the possible isotropy groups are shown to be $(SU(2)\ltimes\mathbb{R}^4)\times\mathbb{R}$, SU(2), $\mathbb{R}^5$, or the identity. The constraints associated with the existence of certain additional Killing spinors are computed, and used to derive numerous solutions. A discussion of the relevance of the formalism to the complete classification of all supersymmetric configurations in d=11 is given.

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