New fixed points of coupled spin chains

In this work we investigate the effect of long-range interactions on critical theories preserving certain symmetries. M copies of SU(N)1 WZW models are coupled with general terms that respect the chiral SU(N) and a Z_M permutation symmetry. To mimic the long-range interactions, a non-local boson is introduced that couples to the order parameter of the individual chains. We derive the RG equations in certain limits where both M and N are large. We then find two fixed points: a stable fixed point decoupled from the external non-local boson, and another critical point that separates a Neel phase induced by the long-range interaction and the stable fixed point. The scaling exponents at the critical points are calculated, and relations to known conformal field theories are discussed. Our work shed light on long-range interaction induced fixed point and boundary criticality problems.