Bethe Ansatz for a Quantum Supercoset Sigma Model

TL;DR

This paper develops integral equations for a supercoset sigma model using the Bethe Ansatz, providing exact results in the coupling constant and connecting to classical equations, with insights into quantum expansions.

Contribution

It introduces integral equations for the supercoset sigma model states, capturing lambda^{-1/2} quantum effects and linking to classical Bethe equations, advancing understanding of integrable superstring models.

Findings

Derived integral equations for large particle density states.

Connected quantum results to classical Bethe equations.

Identified limitations in capturing 1/J effects.

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.