  We systematically study ground state properties of fermionic dipolar gases in
a planar array of one-dimensional potential tubes for an arbitrary orientation
of dipole moments. Using the Luttinger liquid theory with the generalized
Bogoliubov transformation, we calculate the elementary excitations and the
Luttinger scaling exponents for various relevant quantum orders. The complete
quantum phase diagrams for arbitrary polar angle of the dipole moment is
obtained, including charge density wave, p-wave superfluid, inter-tube
gauge-phase density wave, and inter-tube s-wave superfluid, where the last two
breaks the U(1) gauge symmetry of the system (conservation of particle number
in each tube) and occurs only when the inter-tube interaction is larger than
the intra-tube interaction. We then discuss the physical properties of these
many-body phases and their relationship with some solid state systems.
