  We consider circular strings rotating with equal spins S_1=S_2=S in two
orthogonal planes in AdS_5 and suggest that they may be dual to "long" gauge
theory operators built out of self-dual components of gauge field strength. As
was found in hep-th/0404187, the one-loop anomalous dimensions of the such
gauge-theory operators are described by an anti-ferromagnetic XXX_1 spin chain
and scale linearly with length L>>1. We find that in the case of rigid rotating
string both the classical energy E_0 and the 1-loop string correction E_1
depend linearly on the spin S (within the stability region of the solution).
This supports the relation between the rigid rotating string and the
gauge-theory operator corresponding to the maximal-spin (ferromagnetic) state
of the XXX_1 spin chain. The energy of more general rotating and pulsating
strings also happens to scale linearly with both the spin and the oscillation
number. Such solutions should be dual to other lower-spin states of the spin
chain, with the anti-ferromagnetic ground state presumably corresponding to the
string pulsating in two planes with no rotation.
