  We use the SLE$_\kappa$ loop measure to construct a natural representation of
the Virasoro algebra of central charge $c = c(\kappa) \le 1$. In particular, we
introduce a non-degenerate bilinear Hermitian form (not positive-definite)
using the SLE loop measure and show that the representation is (indefinite)
unitary. Our proof relies on the infinitesimal conformal restriction property
of the SLE loop measure.
