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.
Highlights
Conformal field theory (CFT) has attracted considerable interest over the years in problems ranging from high-energy physics to statistical and condensed matter physics [1,2,3]
We have identified an IR massless renormalization group (RG) flow for the SU(N )k WZNW model perturbed by its relevant adjoint primary field
Using a mapping onto k-leg SU(N ) spin ladder and assuming a weak-strong coupling continuity, we have shown that this model has critical properties in the SU(N )1 universality class when N and k have no common divisor
Summary
Conformal field theory (CFT) has attracted considerable interest over the years in problems ranging from high-energy physics to statistical and condensed matter physics [1,2,3]. It will be shown that the SU(N )k perturbed CFT (1) describes the low-energy limit of weakly coupled SU(N ) spin ladder and SU(N ) spin chain models with symmetric rank-k tensor representation. In the simplest k = 2 and N = 3 case we perform a direct approach by means of Gepner’s parafermions (GP) [27] In this respect, we conclude that the SU(3) CFT perturbed by its adjoint primary field enjoys a massless RG flow down to the SU(3) universality class. In the weak-coupling limit |J⊥| ≪ J , one can perform a low-energy approach to deduce the physical properties of the spin ladder (4) In this respect, we will extend the results of Ref. 36 to the general k > 2 case. FIG. 1: (color online) k-leg SU(N ) spin ladder
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