Multi-critical multi-field models: a CFT approach to the leading order

Abstract

We present some general results for the multi-critical multi-field models in d>2 recently obtained using CFT and Schwinger-Dyson methods at perturbative level without assuming any symmetry. Results in the leading non trivial order are derived consistently for several conformal data in full agreement with functional perturbative RG methods. Mechanisms like emergent (possibly approximate) symmetries can be naturally investigated in this framework.

arXiv comment12 pages, 1 figure, Contribution to the Conference QFT2018, Quantum Fields From Fundamental Concepts to Phenomenological Questions, Mainz 26-28 September 2018

References in corpus (25)

• Bounding scalar operator dimensions in 4D CFT
• Solving the 3D Ising Model with the Conformal Bootstrap
• Walking, Weak first-order transitions, and Complex CFTs
• Large Spin Perturbation Theory
• Asymptotic safety guaranteed
• Conformal Bootstrap in Mellin Space
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Bootstrapping critical Ising model on three-dimensional real projective space
• Generalized Wilson-Fisher critical points from the conformal OPE
• Multi-meson Yukawa interactions at criticality
• Epsilon Expansion for Multicritical Fixed Points and Exact Renormalisation Group Equations
• Scalar CFTs and Their Large N Limits
• Leading CFT constraints on multi-critical models in d>2
• Classical equation of motion and Anomalous dimensions at leading order
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• New universality class in three dimensions: The critical Blume-Capel model
• A functional perspective on emergent supersymmetry
• Leading order CFT analysis of multi-scalar theories in d>2
• Spectrum of anomalous dimensions in hypercubic theories
• Multi-critical ${\square }^k$ scalar theories: A perturbative RG approach with $\epsilon$-expansion
• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Platonic Field Theories

Cited by in corpus (13)

• Functional Renormalization and $\overline{\text{MS}}$
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• A multicritical Landau-Potts field theory
• Bounds on multiscalar CFTs in the epsilon expansion
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Infinite distances in multicritical CFTs and higher-spin holography
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• Bubble-resummation and critical-point methods for $\beta$-functions at large $N$
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations