Leading order CFT analysis of multi-scalar theories in d>2

Abstract

We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we just define to admit a Landau-Ginzburg description that includes the most general critical interactions built from monomials of the form ${\varphi }_{i_1}\cdots {\varphi }_{i_m}$. For all such models we analyze to the leading order of the $\epsilon$-expansion the anomalous dimensions of the fields and those of the composite quadratic operators. For models with even $m$ we extend the analysis to an infinite tower of composite operators of arbitrary order. The results are supplemented by the computation of some families of structure constants. We also find the equations which constrain the nontrivial critical theories at leading order and show that they coincide with the ones obtained with functional perturbative RG methods. This is done for the case $m=3$ as well as for all the even models. We ultimately specialize to $S_q$ symmetric models, which are related to the $q$-state Potts universality class, and focus on three realizations appearing below the upper critical dimensions $6$, $4$ and $\frac{10}{3}$, which can thus be nontrivial CFTs in three dimensions.

58 pages; v2: minor clarifications added, to appear in EPJC

References in corpus (12)

• Exact evolution equation for the effective potential
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Conformal Bootstrap in Mellin Space
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Four loop renormalization of the Gross-Neveu model
• Generalized Wilson-Fisher critical points from the conformal OPE
• Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Bootstrapping hypercubic and hypertetrahedral theories in three dimensions
• New universality class in three dimensions: The critical Blume-Capel model
• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Six dimensional Landau-Ginzburg-Wilson theory

Cited by in corpus (19)

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• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• Spectrum of anomalous dimensions in hypercubic theories
• A multicritical Landau-Potts field theory
• Bounds on multiscalar CFTs in the epsilon expansion
• The tri-fundamental quartic model
• Multi-critical multi-field models: a CFT approach to the leading order
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Sextic tensor model in rank $3$ at next-to-leading order
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• Non-perturbative quantum Galileon in the exact renormalization group
• Bubble-resummation and critical-point methods for $\beta$-functions at large $N$
• 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