We show how in the presence of RR two-form field strength the conditions for preserving supersymmetry on six- and seven-dimensional manifolds lead to certain generalizations of monopole equations. For six dimensions the string frame metric is Kahler with the complex structure that descends from the octonions if in addition we assume F-(1,F-1) = 0. The susy generator is a gauge covariantly constant spinor. For seven dimensions the string frame metric is conformal to a G(2) metric if in addition we assume the field strength to obey a self-duality constraint. Solutions to these equations lift to geometries of G(2) and Spin(7) holonomy respectively
Kaste, P., Minasian, R., Petrini, M., Tomasiello, A. (2002). Kaluza-Klein bundles and manifolds of exceptional holonomy. JOURNAL OF HIGH ENERGY PHYSICS, 6(9), 669-683 [10.1088/1126-6708/2002/09/033].
Kaluza-Klein bundles and manifolds of exceptional holonomy
TOMASIELLO, ALESSANDRO
2002
Abstract
We show how in the presence of RR two-form field strength the conditions for preserving supersymmetry on six- and seven-dimensional manifolds lead to certain generalizations of monopole equations. For six dimensions the string frame metric is Kahler with the complex structure that descends from the octonions if in addition we assume F-(1,F-1) = 0. The susy generator is a gauge covariantly constant spinor. For seven dimensions the string frame metric is conformal to a G(2) metric if in addition we assume the field strength to obey a self-duality constraint. Solutions to these equations lift to geometries of G(2) and Spin(7) holonomy respectively
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