Generalized Holonomy of Supergravities with 8 Real Supercharges

TL;DR

This paper characterizes the generalized holonomy groups of ungauged supergravity theories with 8 real supercharges, showing they are contained within a specific subgroup of SL(2,H), and explores implications for classifying supergravity vacua.

Contribution

It establishes a precise mathematical structure for the generalized holonomy groups in supergravity with 8 supercharges and links G-structures to these groups for vacuum classification.

Findings

Holonomy groups are contained in SL(2- u,H) imes{ u H^{2- u}}

Allowed preserved supersymmetries are n=0,4,8

Explicit analysis of solutions in 4, 5, and 6 dimensions

Abstract

We show that the generalized holonomy groups of ungauged supergravity theories with 8 real supercharges must be contained in SL(2-\nu,H)\ltimes{\nu H^{2-\nu}}\subseteq SL(2,H), where SL(2,H) is the generalized structure group. Here n=4\nu is 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.