The algebraic curve of 1-loop planar N=4 SYM

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 AdS5×S5 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 AdS5×S1 and the su(2,2) spin chain agreement of the curves is shown.