Bethe Ansatz for a Quantum Supercoset Sigma Model
Nelia Mann, Joe Polchinski
TL;DR
This work constructs an integrable quantum sigma model based on the OSp(2m+2|2m)/OSp(2m+1|2m) coset and derives exact finite-density Bethe equations in an SU(2) sector from its S-matrix. By taking the n→2 limit, the authors connect the quantum Bethe equations to the classical Kazakov–Marshakov–Minahan–Zarembo equation, revealing two distinct quantum expansion regimes: λ^{-1/2} (worldsheet) and 1/J (finite-size). Their analysis shows the method captures λ^{-1/2} corrections but does not address 1/J corrections, and it highlights the nontrivial role of zero modes in the large-χ limit and their reduction in nonrelativistic regimes. The results illuminate how a quantum-integrable sigma model can mirror aspects of AdS5×S5 dynamics while clarifying limitations and potential extensions toward more string-theoretic settings.
Abstract
We study an integrable conformal OSp(2m + 2|2m) supercoset model as an analog to the AdS_5 X S^5 superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle density 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.