Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-03-06
Nucl.Phys.B764:15-61,2007
Physics
High Energy Physics
High Energy Physics - Theory
52 pages, 10 figures, LaTeX
Scientific paper
10.1016/j.nuclphysb.2006.11.018
We study the quantum Bethe ansatz equations in the O(2n) sigma-model for hysical 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 S^{2n-1} x R_t 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 S^5 x R_t 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.
Gromov Nikolay
Kazakov Vladimir
Sakai Kazuhiro
Vieira Pedro
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