Multi-critical behaviour in a self-dual Josephson junction array –fixed dimension renormalization versus large-N technique

Self-dual Josephson junction arrays are modelled by a theory of N components complex fields coupled to gauge fields. The multi-critical behaviour is analysed through a one loop renormalization group investigation at fixed dimension, which reveals the existence of charged infrared-stable fixed point solutions for large N. Further analysis of the model in the framework of the 1/N expansion confirms that the decoupled fixed point that was stable in the massive regime within the approximate one-loop renormalization group is destabilized. This is ascribed to the special interaction mediated by the mixed Chern-Simons term.