The tri-fundamental quartic model

Abstract

We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2)\times O(N_3)$ transformations, of which the scalar fields form a tri-fundamental representation. We study the renormalization group fixed points at two loops at finite $N$ and in various large-$N$ scaling limits for small $\epsilon$, the latter being either the deviation 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 $\epsilon N^2\gg 1$, we find complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the results of arXiv:1707.03866 ; 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 $\epsilon N\ll 1$, we find again complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the line of stable fixed points of arXiv:1903.03578; at next-to-leading order, this is reduced to a discrete set of stable fixed points. One difference between the short-range and 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.

26 pages, 1 figure

References in corpus (30)

• Critical Phenomena and Renormalization-Group Theory
• Critical behavior of colored tensor models in the large N limit
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Walking, Weak first-order transitions, and Complex CFTs
• Nonperturbative renormalization group approach to frustrated magnets
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• $O(N)$ Random Tensor Models
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Large-n Critical Behavior of O(n)xO(m) Spin Models
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Prismatic Large $N$ Models for Bosonic Tensors
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• Fixed point stability and decay of correlations
• Tensorial Gross-Neveu models
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Line of fixed points in a bosonic tensor model
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Six-loop $\epsilon$ expansion study of three-dimensional $O(n)\times O(m)$ spin models
• Long-range multi-scalar models at three loops
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Leading order CFT analysis of multi-scalar theories in d>2
• The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
• The Euler characteristic correction to the Kaehler potential - revisited
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• Higher melonic theories
• Chiral exponents in O(N) x O(m) spin models at O(1/N^2)
• Bounds on multiscalar CFTs in the epsilon expansion
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• Hints of unitarity at large $N$ in the $O(N{)}^3$ tensor field theory

Cited by in corpus (9)

• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• The F-theorem in the melonic limit
• Remarks on a melonic field theory with cubic interaction
• Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions
• Instability of complex CFTs with operators in the principal series
• Sextic tensor model in rank $3$ at next-to-leading order
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$