Suppose that $(M,E)$ is a compact contact manifold, and that a compact Lie
group $G$ acts on $M$ transverse to the contact distribution $E$. In
arxiv:0712.2431v4, we defined a $G$-transversally elliptic Dirac operator
$\dirac$, constructed using a Hermitian metric $h$ and connection $\nabla$ on
the symplectic vector bundle $E\to M$, whose equivariant index is well-defined
as a generalized function on $G$, and gave a formula for its index.