Generalized Holonomy of Supergravities with 8 Real Supercharges

Abstract

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.

13 pages, 2 tables; 3 references added

References in corpus (2)

• Holonomy and Symmetry in M-theory
• Godel Spacetimes, Abelian Instantons, the Graviphoton Background and other Flacuum Solutions

Cited by in corpus (9)

• The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets
• All timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets
• All solutions of the localization equations for N=2 quantum black hole entropy
• Geometry of four-dimensional Killing spinors
• Classification, geometry and applications of supersymmetric backgrounds
• Maximally supersymmetric G-backgrounds of IIB supergravity
• Higher Order Integrability in Generalized Holonomy
• Erice lectures on "The status of local supersymmetry"
• Symmetry and holonomy in M Theory