  We define multiple-paths Schramm-Loewner evolution ($SLE_\kappa$) in multiply
connected domains when $\kappa\leq 4$ and prove that in annuli, the partition
function is smooth. Moreover, we give up-to-constant estimates for the
partition function of bi-chordal annulus $SLE_\kappa$ measure and we establish
a connection between this measure and two-sided $SLE_\kappa$ in the unit disk.
