Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra

Abstract

We use the SLE${}_{\hat{I}}º$ loop measure to construct a natural representation of the Virasoro algebra of central charge $c=c(\hat{I}º)\le 1$. In particular, we introduce a non-degenerate bilinear Hermitian form (and non 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.

25 pages, to appear in J. Math. Pures Appl