Massless renormalization group flow in SU(N)$_k$ perturbed conformal field theory

TL;DR

This paper studies the low-energy behavior of SU(N)$_k$ conformal field theories perturbed by an adjoint field, predicting a massless flow to SU(N)$_1$ criticality in certain cases, with implications for spin chain models.

Contribution

It extends the understanding of massless renormalization group flows in SU(N)$_k$ theories, generalizing known results for SU(2) and connecting to spin chain physics.

Findings

Predicts massless RG flow from SU(N)$_k$ to SU(N)$_1$ when N and k are coprime.

Provides a direct analysis for the N=3, k=2 case confirming the flow.

Connects the field theory results to SU(N) spin chain models and Haldane's conjecture.

Abstract

We investigate the infrared properties of SU(N)$_k$ conformal field theory perturbed by its adjoint primary field in 1+1 dimensions. The latter field theory is shown to govern the low-energy properties of various SU(N) spin chain problems. In particular, using a mapping onto k-leg SU(N) spin ladder, a massless renormalization group flow to SU(N)$_1$ criticality is predicted when N and k have no common divisor. The latter result extends the well-known massless flow between SU(2)$_k$ and SU(2)$_1$ Wess-Zumino-Novikov-Witten theories when k is odd in connection to the Haldane's conjecture on SU(2) Heisenberg spin chains. A direct approach is presented in the simplest N=3 and k=2 case to investigate the existence of this massless flow.