Supersymmetric Cycles in Exceptional Holonomy Manifolds and Calabi-Yau 4-Folds

Details Supersymmetric Cycles in Exceptional Holonomy Manifolds and Calabi-Yau 4-Folds Supersymmetric Cycles in Exceptional Holonomy Manifolds and Calabi-Yau 4-Folds

1996-08-18

arxiv.org/abs/hep-th/9608116v2

Nucl.Phys.B480:225-238,1996

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, latex, no figures. Clarifying remarks on the Super-Yang-Mills approach added

Scientific paper

10.1016/S0550-3213(96)00491-9

We derive in the SCFT and low energy effective action frameworks the necessary and sufficient conditions for supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau 4-folds. We show that the Cayley cycles in $Spin(7)$ holonomy eight-manifolds and the associative and coassociative cycles in $G_2$ holonomy seven-manifolds preserve half of the space-time supersymmetry. We find that while the holomorphic and special Lagrangian cycles in Calabi-Yau 4-folds preserve half of the space-time supersymmetry, the Cayley submanifolds are novel as they preserve only one quarter of it. We present some simple examples. Finally, we discuss the implications of these supersymmetric cycles on mirror symmetry in higher dimensions.

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