Finite Size Scaling and Conformal Curves
  In this letter we investigate the finite size scaling effect on SLE($\kappa,\rho$) and boundary conformal field theories and find the effect of fixing some boundary conditions on the free energy per length of SLE($\kappa,\rho$). As an application, we will derive the entanglement entropy of quantum systems in critical regime in presence of boundary operators. 
M. A. Rajabpour, S. Moghimi-Araghi