We present a spectrum of highly excited charmonium mesons up to around 4.5
GeV calculated using dynamical lattice QCD. Employing novel computational
techniques and the variational method with a large basis of carefully
constructed operators, we extract and reliably identify the continuum spin of
an extensive set of excited states, states with exotic quantum numbers (0+-,
1-+, 2+-) and states with high spin. Calculations are performed on two lattice
volumes with pion mass approximately 400 MeV and the mass determinations have
high statistical precision even for excited states. We discuss the results in
light of experimental observations, identify the lightest 'supermultiplet' of
hybrid mesons and comment on the phenomenological implications of the spectrum
of exotic mesons.Comment: 33 pages, 17 figures; v2: minor changes to reflect published versio