  We compute the effects of strong Hubbardlike local electronic interactions on
three-dimensional four-component massless Dirac fermions, which in a
noninteracting system possess a microscopic global U(1)$\otimes$SU(2) chiral
symmetry. A concrete lattice realization of such chiral Dirac excitations is
presented, and the role of electron-electron interactions is studied by
performing a field theoretic renormalization group (RG) analysis, controlled by
a \emph{small} parameter $\epsilon$ with $\epsilon=d-1$, about the
lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed
point, the system supports four quantum critical and four bicritical points at
nonvanishing interaction couplings $\sim \epsilon$. Even though the chiral
symmetry is absent in the interacting model, it gets restored (either partially
or fully) at various RG fixed points as emergent phenomena. A representative
cut of the global phase diagram displays a confluence of scalar and
pseudoscalar excitonic and superconducting (such as the $s$-wave and $p$-wave)
mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry
between two excitonic masses for repulsive interactions and (b) pseudospin
SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting
masses for attractive interactions. Finally, we perturbatively study the
effects of \emph{weak} rotational symmetry breaking on the stability of various
RG fixed points.
