Bethe Ansatz for Lattice Analogues of $N=2$ Superconformal Theories

TL;DR

This paper applies Bethe Ansatz techniques to lattice models related to $N=2$ superconformal theories, calculating spectra and critical properties that match theoretical predictions, thus bridging lattice models and superconformal field theories.

Contribution

It introduces Bethe Ansatz methods to analyze lattice analogues of $N=2$ superconformal models and computes their spectra and critical parameters.

Findings

Calculated the spectrum of the transfer matrix for these lattice models.

Determined the central charge and conformal weights from finite-size corrections.

Results agree with predictions from superconformal field theory.

Abstract

The critical Boltzmann weights for lattice analogues of the $N=2$ superconformal coset models $\frac{G_1 \times SO(dim(G/H))}{H}$ were given in \cite{nick}. In this paper Bethe Ansatz methods are employed to calculate the spectrum of the transfer matrix obtained from these Boltzmann weights. {}From this the central charge and conformal weights are obtained by calculating finite-size corrections to the free energy per site. The results agree with those obtained from the superconformal model.