  We derive and analyze the effective low-energy theory for interacting
electrons in a cylindrical nanowire made of a strong topological insulator.
Three different approaches provide a consistent picture for the band structure,
where surface states forming inside the bulk gap correspond to one-dimensional
bands indexed by total angular momentum. When a half-integer magnetic flux
pierces the nanowire, we find a strongly correlated helical Luttinger liquid
topologically protected against weak disorder. We describe how transport
experiments can detect this state.
