Topologican Gauging of N=16 Supergravity in Three-Dimensions

TL;DR

This paper introduces a topologically non-trivial generalization of gauged N=16 supergravity in three dimensions, incorporating BF and Chern-Simons terms, and explores its implications for extended supergravity theories.

Contribution

It presents a novel topological gauging of N=16 supergravity using BF and Chern-Simons terms, with a propagating vector field, differing from conventional approaches.

Findings

Formulation based on BF and Chern-Simons terms for SO(16) gauge field.

Propagation of an additional vector field B_ield.

Application to N=9 supergravity and extended supergravity theories.

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 \sigma-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 \pi_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 \sigma-model on the coset F_4 / SO(9), and a new BF-Chern-Simons theory coupled to ^\forall N extended supergravity.