  Recently, an impressive agreement was found between anomalous dimensions of
certain operators in N=4 SYM and rotating strings with two angular momenta in
the bulk of AdS5xS5. A one-loop field theory computation, which involves
solving a Heisenberg chain by means of the Bethe ansatz agrees with the large
angular momentum limit of a rotating string. We point out that the Heisenberg
chain can be equally well solved by using a sigma model approach. Moreover we
also show that a certain limit, akin to the BMN limit, leads exactly to the
same sigma model for a string rotating with large angular momentum. The
agreement is then at the level of the action. As an upshot we propose that the
rotating string should be identified with a coherent, semi-classical state
built out of the eigenstates of the spin chain. The agreement is then complete.
For example we show that the mean value of the spin <S> gives, precisely, the
position of the string in the bulk. This suggests a more precise formulation of
the AdS/CFT correspondence in the large-N limit and also indicates a way to
obtain string theory duals of other gauge theories.
