Bethe ansatz for a quantum supercoset sigma model

We study an integrable conformal $\mathrm{OSp}(2m+2|2m)$ supercoset model as an analog to the $\mathrm{Ad}{\mathrm{S}}_5\times {\mathrm{S}}^5$ superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle number in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the well-studied classical limit, the ${\lambda }^{-1/2}$ effects and the $1/J$ effects. Our approach captures the first type, but not the second.

Figure 1

Terms in the S-matrix