Slow-string limit and "antiferromagnetic" state in AdS/CFT duality

We discuss a slow-moving limit of a rigid circular equal-spin solution on R×S3. We suggest that the solution with the winding number equal to the total spin approximates the quantum string state dual to the maximal-dimension "antiferromagnetic" state of the SU(2) spin chain on the gauge-theory side. An expansion of the string action near this solution leads to a weakly-coupled system of a sine-Gordon model and a free field. We show that a similar effective Hamiltonian appears in a certain continuum limit from the half-filled Hubbard model that was recently suggested to describe the all-order dilatation operator of the dual gauge theory in the SU(2) sector. We also discuss some other slow-string solutions with one spin component in AdS5 and one in S5.