Abstract:The path integral of a conformal field theory on a bordered Riemann surface defines a state in a Hilbert space on this boundary. Over the ideal boundary, the Hausdorff dimension may be less than one. The integral representing the flux over the ideal boundary is evaluated through a generalization of the residue theorem. The identification of the state for infinite-genus surfaces with the vacuum state with a perturbative vacuum is distinguished from the Hilbert space on ideal boundaries of nonzero linear measure… Show more
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