  In 5d transition metal oxides such as the iridates, novel properties arise
from the interplay of electron correlations and spin-orbit interactions. We
investigate the electronic structure of the pyrochlore iridates, (such as
Y$_{2}$Ir$_{2}$O$_{7}$) using density functional theory, LDA+U method, and
effective low energy models. A remarkably rich phase diagram emerges on tuning
the correlation strength U. The Ir magnetic moment are always found to be
non-collinearly ordered. However, the ground state changes from a magnetic
metal at weak U, to a Mott insulator at large U. Most interestingly, the
intermediate U regime is found to be a Dirac semi-metal, with vanishing density
of states at the Fermi energy. It also exhibits topological properties -
manifested by special surface states in the form of Fermi arcs, that connect
the bulk Dirac points. This Dirac phase, a three dimensional analog of
graphene, is proposed as the ground state of Y$_{2}$Ir$_{2}$O$_{7}$ and related
compounds. A narrow window of magnetic `axion' insulator, with axion parameter
$\theta=\pi$, may also be present at intermediate U. An applied magnetic field
induces ferromagnetic order and a metallic ground state.
