  We study $(1+1)$-dimensional p-wave holographic superconductors described by
three dimensional Einstein-Maxwell gravity coupled to a massive complex vector
field in the context of $AdS_3/CFT_2$ correspondence. In the probe limit where
the backreation of matter fields is neglected, we show that there occurs a
formation of a vector hair around the black hole below a certain critical
temperature. In the dual strongly coupled $(1+1)$-dimensional boundary theory,
this holographically corresponds to the formation of a charged vector
condensate spontaneously breaking both the $U(1)$ and $SO(1,1)$ symmetries. We
numerically compute the ac conductivity for the superconducting phase of the
boundary field theory and find that the presence of a magnetic moment term in
the dual bulk theory effects the conductivity in the boundary field theory.
