  The algebraic curve for the psu (2,2|4) quantum spin chain is determined from
the thermodynamic limit of the algebraic Bethe ansatz. The Hamiltonian of this
spin chain has been identified with the planar 1-loop dilatation operator of
N=4 SYM. In the dual AdS_5 x S^5 string theory, various properties of the data
defining the curve for the gauge theory are compared to the ones obtained from
semiclassical spinning-string configurations, in particular for the case of
strings on AdS_5 x S^1 and the su(2,2) spin chain agreement of the curves is
shown.
