Strings as multi-particle states of quantum sigma-models Original Research Article

We study the quantum Bethe ansatz equations in the image sigma-model for physical particles on a circle, with the interaction given by the Zamolodchikovsʹ S-matrix, in view of its application to quantization of the string on the image space. For a finite number of particles, the system looks like an inhomogeneous integrable image spin chain. Similarly to image 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 image 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 image super-Yang–Mills theory. We discuss the prospects of generalization of these Bethe equations to the full superstring sigma-model.