Finite Size Scaling and Conformal Curves

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In this letter we investigate the finite size scaling effect on SLE($κ,ρ$) and boundary conformal field theories and find the effect of fixing some boundary conditions on the free energy per length of SLE($κ,ρ$). As an application, we will derive the entanglement entropy of quantum systems in critical regime in presence of boundary operators.
5 pages, No figures

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