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We use the SLE_κ loop measure to construct a natural representation of the Virasoro algebra of central charge c = c(κ) ≤ 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.
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Gordina et al. (2024) studied this question.
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