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(N-1) x O(N-2) x O(N-3) transformations, of which the scalar fields form a trifundamcntal representation. We study the renormalization group fixed points at two loops at finite N and in various large-N scaling limits for small e, 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 N-i = N for i = 1, 2, 3, we study the subleading corrections to previously known fixed points. In the short-range model, for epsilon N-2 >> 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).]; the main novelty at next-toleading 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 epsilon N << 1, 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) 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.

Automated summary

The study examines the renormalization group fixed points of a multiscalar field theory under finite N conditions and in various large-N scaling limits. Different behaviors between the short-range and long-range models in terms of critical exponents at leading and next-to-leading orders are observed.