Lattice Analogues of $N=2$ Superconformal Models via Quantum Group Truncation

TL;DR

This paper constructs lattice models that replicate $N=2$ superconformal coset models in the continuum limit by twisting transfer matrices and modifying quantum group truncations, linking lattice and conformal field theories.

Contribution

It introduces a novel lattice formulation of $N=2$ superconformal models using quantum group truncation and transfer matrix twisting, connecting lattice models with superconformal field theories.

Findings

Lattice models correspond to $N=2$ superconformal coset models in the continuum limit.

Natural order parameters are the chiral primary fields.

Integrable perturbations are incorporated into the lattice framework.

Abstract

We obtain lattice models whose continuum limits correspond to $N=2$ superconformal coset models. This is done by taking the well known vertex model whose continuum limit is the $G \times G/G$ conformal field theory, and twisting the transfer matrix and modifying the quantum group truncation. We find that the natural order parameters of the new models are precisely the chiral primary fields. The integrable perturbations of the conformal field theory limit also have natural counterparts in the lattice formulation, and these can be incorporated into an affine quantum group structure. The topological, twisted $N=2$ superconformal models also have lattice analogues, and these emerge as an intermediate part of our analysis.