Softness of Supersymmetry Breaking on the Orbifold T²/Z₂

We consider supersymmetry breaking due to a Scherk-Schwarz twist or localized mass terms in 6d ${\cal N}=1$ supersymmetric gauge theory compactified on the orbifold $T^2/Z_2$. We show that the Scherk-Schwarz breaking in 6d is equivalent to the localized breaking with mass terms along the lines in extra dimensions. In the presence of the considered supersymmetry breaking, we find that there arises a finite one-loop mass correction to a brane scalar due to the KK modes of bulk gauge fields.