Critical fluctuations in $N$-component superconductor models

Inspired by recent conflicting views on the order of the phase transition from an antiferromagnetic N\'eel state to a spin liquid or valence bond solid, we use the functional renormalization group to reconsider the $N$-component superconductor models, in which a dynamic gauge field is minimally coupled to $N$ bosonic complex fields. In contrast to previous work, we only expand in covariant derivatives and use a truncation in which the full field dependence of all wave-function renormalization functions is kept. As a consequence, we find non-trivial RG fixed points for all positive integer $N$.