Massless renormalization group flow in SU(N)$_k$ perturbed conformal field theory
P. Lecheminant
TL;DR
The paper addresses the infrared fate of SU(N)_k WZNW conformal field theories perturbed by their adjoint primary field, motivated by SU(N) spin chains and ladders. It develops a mapping to a k-leg SU(N) spin ladder and employs continuum, strong-coupling, and parafermionic analyses to argue for a massless renormalization group flow to SU(N)_1 when gcd(N,k)=1. A concrete demonstration is provided for the N=3, k=2 case using Gepner's parafermions, showing the IR fixed point is SU(3)_1 and that Tr adj flows to the SU(3)_1 current. These results generalize the SU(2) Haldane-type massless flows and offer a framework for understanding SU(N) spin systems with higher representations.
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.