Topologican Gauging of N=16 Supergravity in Three-Dimensions

Abstract

We present a topologically non-trivial generalization of gauged N=16 supergravity on the coset E_8 / SO(16) in three-dimensions. This formulation is based on a combination of BF-term and a Chern-Simons term for an SO(16) gauge field A_\m{}^{I J}. The fact that an additional vector field B_\m{}^{I J} is physical and propagating with couplings to σ-model fields makes our new gauging non-trivial and different from the conventional one. Even though the field strength of the A_\m{}^{I J}-field vanishes on-shell, the action is topologically non-trivial due to non-vanishing π_3-homotopy. We also present an additional modifications by an extra Chern-Simons term. As by-products, we give also an application to N=9 supergravity coupled to a σ-model on the coset F_4 / SO(9), and a new BF-Chern-Simons theory coupled to ^\forall N extended supergravity.