Strings as multi-particle states of quantum sigma-models

Nikolay Gromov (1) , Vladimir Kazakov (2, 3) , Kazuhiro Sakai (2) , Pedro Vieira (4)

1 St. Petersburg Nuclear Physics Institute
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
3 UPMC - Université Pierre et Marie Curie - Paris 6
4 MPIA - Max-Planck-Institut für Astronomie

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 S×R 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×R 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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Nikolay Gromov, Vladimir Kazakov, Kazuhiro Sakai, Pedro Vieira. Strings as multi-particle states of quantum sigma-models. Nuclear Physics B, 2007, 764, pp.15-61. ⟨10.1016/J.NUCLPHYSB.2006.11.018⟩. ⟨hal-00717901⟩