Abstract :
The algebraic curve for the image 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 image SYM. In the dual image 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 image and the image spin chain agreement of the curves is shown.