Strings as multi-particle states of quantum sigma-models

We study the quantum Bethe ansatz equations in the O(2n) sigma-model for physical particles on a circle, with the interaction given by the Zamolodchikovs' S-matrix, in view of its application to quantization of the string on the S2n−1×Rt space. For a finite number of particles, the system looks like an inhomogeneous integrable O(2n) spin chain. Similarly to OSp(2m+n|2m) conformal sigma-model considered by Mann and Polchinski, we reproduce in the limit of large density of particles the finite gap Kazakov-Marshakov-Minahan-Zarembo solution for the classical string and its generalization to the S5×Rt sector of the Green-Schwarz-Metsaev-Tseytlin superstring. We also reproduce some quantum effects: the BMN limit and the quantum homogeneous spin chain similar to the one describing the bosonic sector of the one-loop N=4 super-Yang-Mills theory. We discuss the prospects of generalization of these Bethe equations to the full superstring sigma-model.