Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion

Abstract

Fixed points for scalar theories in $4-\epsilon$, $6-\epsilon$ and $3-\epsilon$ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings. The original maximal symmetry, $O(N)$, is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the $a$-theorem are used to help classify potential fixed points. At lowest order in the $\epsilon$-expansion it is shown that at fixed points there is a lower bound for $a$ which is saturated at bifurcation points.

v1: 55 pages. v2: 58 pages; new fixed points in 4-ε dimensions, further discussion of large-N behaviour in 3-ε dimensions, additional references; v3: Typos fixed; v4: Added references. Version to appear in JHEP; v5: Minor emendations, references added. v6: 60 pages; typos fixed, some new results and references added. v7: 61 pages; some additions in section 5 and appendix B

References in corpus (8)

• A Mellin space approach to the conformal bootstrap
• Conformal Bootstrap in Mellin Space
• Mellin space bootstrap for global symmetry
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Fixed point stability and decay of correlations
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap
• The a-function in three dimensions: beyond leading order
• On the Renormalization Group Flow in Two Dimensional Superconformal Models

Cited by in corpus (54)

• Prismatic Large $N$ Models for Bosonic Tensors
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• Scalar CFTs and Their Large N Limits
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II
• Large $N_f$ quantum field theory
• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Coupled minimal models revisited
• Line Defect RG Flows in the $\epsilon$ Expansion
• Bootstrapping MN and Tetragonal CFTs in Three Dimensions
• Long-range multi-scalar models at three loops
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Seeking SUSY fixed points in the $4-\epsilon$ expansion
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• Anomalous dimensions for ${\varphi }^n$ in scale invariant $d=3$ theory
• Theory of a continuous bandwidth-tuned Wigner-Mott transition
• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
• Leading order CFT analysis of multi-scalar theories in d>2
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• Tensor $O(N)$ model near six dimensions: fixed points and conformal windows from four loops
• Spectrum of anomalous dimensions in hypercubic theories
• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• Ginzburg-Landau Description and Emergent Supersymmetry of the $(3,8)$ Minimal Model
• Melonic Dominance in Subchromatic Sextic Tensor Models
• A multicritical Landau-Potts field theory
• Ising model close to $d=2$
• The tri-fundamental quartic model
• Disordered vector models: from higher spins to incipient strings
• Bounds on multiscalar CFTs in the epsilon expansion
• Platonic Field Theories
• Bootstrapping Mixed MN Correlators in 3D
• Multi-critical multi-field models: a CFT approach to the leading order
• Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions
• Remarks on a melonic field theory with cubic interaction
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• The tricritical Ising CFT and conformal bootstrap
• 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
• Anomalous Dimensions in Hypercubic Theories
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• Dilaton in scalar QFT: a no-go theorem in $4-\epsilon$ and $3-\epsilon$ dimensions
• Classifying irreducible fixed points of five scalar fields in perturbation theory
• Emergent Supersymmetry at Large $N$
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O($N$) models at large $N$
• Note on surface defects in multiscalar critical models
• Revisiting the ${\varphi }^6$ Theory in Three Dimensions at Large $N$