  Anatase TiO$_2$ is among the most studied materials for light-energy
conversion applications, but the nature of its fundamental charge excitations
is still unknown. Yet it is crucial to establish whether light absorption
creates uncorrelated electron-hole pairs or bound excitons and, in the latter
case, to determine their character. Here, by combining steady-state
angle-resolved photoemission spectroscopy and spectroscopic ellipsometry with
state-of-the-art ab initio calculations, we demonstrate that the direct optical
gap of single crystals is dominated by a strongly bound exciton rising over the
continuum of indirect interband transitions. This exciton possesses an
intermediate character between the Wannier-Mott and Frenkel regimes and
displays a peculiar two-dimensional wavefunction in the three-dimensional
lattice. The nature of the higher-energy excitations is also identified. The
universal validity of our results is confirmed up to room temperature by
observing the same elementary excitations in defect-rich samples (doped single
crystals and nanoparticles) via ultrafast two-dimensional deep-ultraviolet
spectroscopy.
