Scaling limit of the ${\cal Z}_2$ invariant inhomogeneous six-vertex model

TL;DR

This paper investigates the critical behavior of an inhomogeneous six-vertex model, revealing its continuum limit is described by a gauged SL(2) WZW model, extending previous conjectures about its relation to black hole sigma models.

Contribution

It provides a detailed analysis of the scaling limit of an inhomogeneous six-vertex model, using numerical and analytic methods to identify its continuum field theory description.

Findings

Critical behavior described by gauged SL(2) WZW model

Revises previous conjecture linking lattice model to black hole sigma model

Extends understanding of inhomogeneous six-vertex models in critical regime

Abstract

The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as the powerful analytic technique of the ODE/IQFT correspondence. The results indicate that the critical behaviour of the lattice system is described by the gauged ${\rm SL}(2)$ WZW model with certain boundary and reality conditions imposed on the fields. Our proposal revises and extends the conjectured relation between the lattice system and the Euclidean black hole non-linear sigma model that was made in the 2011 paper of Ikhlef, Jacobsen and Saleur.