Finite Size Scaling and Conformal Curves

Abstract

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.

5 pages, No figures