  We present a Lagrangian formulation for ${\cal N}=8$ superconformal field
theories in three spacetime dimensions that is general enough to encompass
infinite-dimensional gauge algebras that generally go beyond Lie algebras. To
this end we employ Chern-Simons theories based on Leibniz algebras, which give
rise to L$_{\infty}$ algebras and are defined on the dual space $\frak{g}^*$ of
a Lie algebra $\frak{g}$ by means of an embedding tensor map $\vartheta
:\frak{g}^*\rightarrow \frak{g}$. We show that for the Lie algebra
$\frak{sdiff}_3$ of volume-preserving diffeomorphisms on a 3-manifold there is
a natural embedding tensor defining a Leibniz algebra on the space of
one-forms. Specifically, we show that the cotangent bundle to any 3-manifold
with a volume-form carries the structure of a (generalized) Courant algebroid.
The resulting ${\cal N}=8$ superconformal field theories are shown to be
equivalent to Bandos-Townsend theories. We show that the theory based on $S^3$
is an infinite-dimensional generalization of the Bagger-Lambert-Gustavsson
model that in turn is a consistent truncation of the full theory. We also
review a Scherk-Schwarz reduction on $S^2\times S^1$, which gives the
super-Yang-Mills theory with gauge algebra $\frak{sdiff}_2$, and we construct
massive deformations.
