  We obtain (2+1) dimensional p-wave holographic superconductors from charged
Born-Infeld black holes in the presence of massive charged vector fields in a
bulk $AdS_4$ Einstein-Born-Infeld theory through the $AdS_4$-$CFT_3$
correspondence. Below a certain critical transition temperature the charged
black hole develops vector hair that corresponds to charged vector condensate
in the strongly coupled (2+1) dimensional boundary field theory that breaks
both the $U(1)$ symmetry as well as the rotational invariance. The holographic
free energy is computed for the boundary field theory which shows that the
vector order parameter exhibits a rich phase structure involving zeroth order,
first order, second order and retrograde phase transitions for different values
of the backreaction and the Born-Infeld parameters. We numerically compute the
ac conductivity for the p-wave superconducting phase of the strongly coupled
(2+1) dimensional boundary field theory which also depends on the relative
values of the parameters in the theory.
