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We investigate transport properties of a superconducting junction of many ($N\ge 2$) one-dimensional quantum wires. We include the effectofelectron-electroninteraction within the one-dimensional quantum wire using a weak interactionrenormalization group procedure. Due to the proximity effect, transport acrossthe junction occurs via direct tunneling as well as via the crossed Andreevchannel. We find that the fixed point structure of this system is far more richthan the fixed point structure of a normal metal$-$superconductor junction ($N= 1$), where we only have two fixed points - the fully insulating fixed pointor the Andreev fixed point. Even a two wire (N=2)system with a superconductingjunction i.e. a normalmetal$-$superconductor$-$normal metal structure, hasnon-trivialfixed points with intermediate transmissions and reflections. Wealso include electron-electron interaction induced back-scattering in thequantum wires in our study and hence obtain non-Luttinger liquid behaviour. Itis interesting to note that {\textsl{(a)}} effects due to inclusion ofelectron-electron interaction induced back-scattering in the wire, and{\textsl{(b)}} competition between the charge transport via the electron andhole channels across the junction, give rise to a non-monotonic behavior ofconductance as a functionof temperature. We also find that transport across thejunction depends on two independent interaction parameters. The first one isdue to the usual correlations coming from Friedel oscillations for spin-fullelectrons giving rise to the well-known interaction parameter (${{\alpha =(g_2-2g_1)/2 \pi \hbar v_F}}$). The second one arises due to the scatteringinduced by the proximity of the superconductor and is given by(${{\alpha^\prime= (g_2 + g_1)/2 \pi \hbar v_F}}$).

Renormalization group study of transport through a superconducting junction of multiple one-dimensional quantum wires