  The bulk band structure of Bi$_2$Te$_3$ has been determined by angle-resolved
photoemission spectroscopy and compared to first-principles calculations. We
have performed calculations using the local density approximation (LDA) of
density functional theory and the one-shot $GW$ approximation within the
all-electron full-potential linearized augmented-plane-wave (FLAPW) formalism,
fully taking into account spin-orbit coupling. Quasiparticle effects produce
significant changes in the band structure of \bite~when compared to LDA.
Experimental and calculated results are compared in the spectral regions where
distinct differences between the LDA and $GW$ results are present. Overall a
superior agreement with $GW$ is found, highlighting the importance of many-body
effects in the band structure of this family of topological insulators.
