2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104622In 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 figuresHigh Energy Physics - Theorytext