Generalized Holonomy of Supergravities with 8 Real Supercharges

We show that the generalized holonomy groups of ungauged supergravity theories with 8 real supercharges must be contained in SL(2-ν,H)\ltimes{νH^{2-ν}}\subseteq SL(2,H), where SL(2,H) is the generalized structure group. Here n=4νis the number of preserved supersymmetries, so the allowed values are limited to n=0,4,8. In particular, solutions of ungauged supergravities in four, five and six dimensions are examined and found to explicitly follow this pattern. We also argue that the G-structure has to be a subgroup of this generalized holonomy group, which may provide a possible classification for supergravity vacua with respect to the number of supercharges.

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