Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2)k Theory Using the Truncated Conformal Spectrum Approach

TL;DR

This study investigates the non-integrable perturbed SU(2)_k WZNW theory using the truncated conformal spectrum approach, revealing its low-energy behavior varies with the coupling sign and parity of k, linking to known models.

Contribution

It applies the TCSA+RG method to analyze a non-integrable perturbed WZNW model, providing new insights into its low-energy phases and their dependence on parameters.

Findings

For even k, the low-energy theory is equivalent to the massive O(3) sigma model.

For odd k, evidence suggests the low-energy theory is critical.

The low-energy behavior is sensitive to the sign of the coupling constant λ.

Abstract

We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at $k\gg 1$. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, $\lambda$. Moreover for $\lambda>0$ this behavior depends on whether $k$ is even or odd. With $k$ even, we find definitive evidence that the model at low energies is equivalent to the massive $O(3)$ sigma model. For $k$ odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.