Strings as Multi-Particle States of Quantum Sigma-Models

TL;DR

This paper investigates the quantum Bethe ansatz equations in the O(2n) sigma-model, connecting finite particle systems to classical string solutions and quantum effects, with implications for superstring quantization.

Contribution

It derives and analyzes Bethe ansatz equations for the O(2n) sigma-model, linking quantum integrable systems to classical string solutions and quantum effects.

Findings

Reproduces classical string solutions in the large density limit.

Captures quantum effects like the BMN limit.

Establishes a connection to the spin chain models in gauge theories.

Abstract

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.