Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions

Abstract

We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$ dimensions. As expected by the paradigm of universality, each class is uniquely characterized by its symmetry group and by a set of its scaling properties, neither of which are built-in by the formalism but instead emerge nontrivially as outputs of our computations. For three fields, we find several solutions mostly with discrete symmetries. These are nontrivial conformal field theory candidates in less than six dimensions, one of which is a new perturbatively unitary critical model.

arXiv comment8 pages; to appear on Phys. Rev. D

References in corpus (20)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Solving the 3D Ising Model with the Conformal Bootstrap
• Derivative Expansion of the Exact Renormalization Group
• Walking, Weak first-order transitions, and Complex CFTs
• Large Spin Perturbation Theory
• Conformal Bootstrap in Mellin Space
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Generalized Wilson-Fisher critical points from the conformal OPE
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• Epsilon Expansion for Multicritical Fixed Points and Exact Renormalisation Group Equations
• Leading CFT constraints on multi-critical models in d>2
• A challenge to the $a$-theorem in six dimensions
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• Leading order CFT analysis of multi-scalar theories in d>2
• The a-function in six dimensions
• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Multi-critical ${\square }^k$ scalar theories: A perturbative RG approach with $\epsilon$-expansion
• Renormalization of multicritical scalar models in curved space

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• Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories
• A multicritical Landau-Potts field theory
• Remarks on a melonic field theory with cubic interaction
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories