Trifundamental quartic model

We consider a multiscalar field theory either with short-range or long-range free action and quartic interactions that are invariant under $O({N}_{1})\ifmmode\times\else\texttimes\fi{}O({N}_{2})\ifmmode\times\else\texttimes\fi{}O({N}_{3})$ transformations, of which the scalar fields form trifundamental representation. study renormalization group fixed points at two loops finite $N$ in various large-$N$ scaling limits for small $\ensuremath{\epsilon}$, latter being deviation from critical dimension propagator. In particular, homogeneous case ${N}_{i}=N$ $i=1$, 2, 3, we subleading corrections to previously known points. model, $\ensuremath{\epsilon}{N}^{2}\ensuremath{\gg}1$, find complex nonzero tetrahedral coupling leading order reproduce results Giombi et al. [Phys. Rev. D 96, 106014 (2017).]; main novelty next-to-leading is exponents acquire real part, thus allowing correct identification some as IR stable. $\ensuremath{\epsilon}N\ensuremath{\ll}1$, again line stable Benedetti [J. High Energy Phys. 06 (2019) 053]; order, this reduced discrete set One difference between cases former purely imaginary gain part while situation reversed.