Trifundamental quartic model

We consider a multiscalar field theory either with short-range or long-range free action and with quartic interactions that are invariant under O(N1)×O(N2)×O(N3) transformations, of which the scalar fields form a trifundamental representation. We study the renormalization group fixed points at two loops at finite N and in various large-N scaling limits for small ϵ, the latter being the deviation either from the critical dimension or from the critical scaling of the free propagator. In particular, for the homogeneous case Ni=N for i=1, 2, 3, we study the subleading corrections to previously known fixed points. In the short-range model, for ϵN2≫1, we find complex fixed points with nonzero tetrahedral coupling that at leading order reproduce the results of Giombi et al. [Phys. Rev. D 96, 106014 (2017).PRVDAQ2470-001010.1103/PhysRevD.96.106014]; the main novelty at next-to-leading order is that the critical exponents acquire a real part, thus allowing a correct identification of some fixed points as IR stable. In the long-range model, for ϵN1, we find again complex fixed points with nonzero tetrahedral coupling that at leading order reproduce the line of stable fixed points of Benedetti et al. [J. High Energy Phys. 06 (2019) 053JHEPFG1029-847910.1007/JHEP06(2019)053]; at next-to-leading order, this is reduced to a discrete set of stable fixed points. One difference between the short-range and the long-range cases is that in the former the critical exponents are purely imaginary at leading order and gain a real part at next-to-leading order, while for the latter the situation is reversed.