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We use the SLE_ loop measure to construct a natural representation of the Virasoro algebra of central charge c = c () 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.
Gordina et al. (Fri,) studied this question.