The Epsilon-Expansion from Conformal Field Theory

Abstract

Conformal multiplets of $\varphi$ and ${\varphi }^3$ recombine at the Wilson-Fisher fixed point, as a consequence of the equations of motion. Using this fact and other constraints from conformal symmetry, we reproduce the lowest nontrivial order results for the anomalous dimensions of operators, without any input from perturbation theory.

arXiv comment24 pages; v2 - references added, minor changes; v3 - refs and comments added, misprints corrected, version to appear in J.Phys.A

References in corpus (53)

• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Four Point Functions and the Operator Product Expansion
• Infinite Chiral Symmetry in Four Dimensions
• Conformal Partial Waves and the Operator Product Expansion
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• The Analytic Bootstrap and AdS Superhorizon Locality
• Projectors, Shadows, and Conformal Blocks
• The Bootstrap Program for Boundary CFT_d
• Bootstrapping the O(N) Vector Models
• Spinning Conformal Blocks
• OPE Convergence in Conformal Field Theory
• Bounds on 4D Conformal and Superconformal Field Theories
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Radial Coordinates for Conformal Blocks
• The $(2,0)$ superconformal bootstrap
• Universal Constraints on Conformal Operator Dimensions
• More constraining conformal bootstrap
• Bootstrapping the 3d Ising twist defect
• Conformal Partial Waves: Further Mathematical Results
• W Symmetry in six dimensions
• Bounds in 4D Conformal Field Theories with Global Symmetry
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
• Conformal Field Theories in Fractional Dimensions
• Central Charge Bounds in 4D Conformal Field Theory
• Universal anomalous dimensions at large spin and large twist
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Diagonal Limit for Conformal Blocks in d Dimensions
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Bootstrapping SCFTs with Four Supercharges
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• The superconformal bootstrap for structure constants
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Constraining conformal field theories with a higher spin symmetry
• Current OPEs in Superconformal Theories
• A Semidefinite Program Solver for the Conformal Bootstrap
• More on La Grande Bouffe: towards higher spin symmetry breaking in AdS
• Generalized bootstrap equations for N=4 SCFT
• Conformal Bootstrap in Three Dimensions?
• On the four-point function of the stress-energy tensors in a CFT
• Generalized Additivity in Unitary Conformal Field Theories
• Constraining conformal field theories with a higher spin symmetry in d=4
• Superembedding methods for 4d N=1 SCFTs
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Superembedding Methods for Current Superfields
• OPE convergence in non-relativistic conformal field theories
• Bootstrapping the $\cN=1$ SCFT in three dimensions
• (No) Bootstrap for the Fractal Ising Model
• Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap

Cited by in corpus (11)

• Higher-point conformal blocks and entanglement entropy in heavy states
• $\epsilon$-Expansion in the Gross-Neveu Model from Conformal Field Theory
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Anomalous dimensions of spinning operators from conformal symmetry
• On (Un)Broken Higher-Spin Symmetry in Vector Models
• Broken current anomalous dimensions, conformal manifolds and RG flows
• The masses of higher spin fields on AdS_4 and conformal perturbation theory
• Holomorphic primary fields in free CFT4 and Calabi-Yau orbifolds
• Relating diagrammatic expansion with conformal correlator expansion
• Critical two-point correlation functions and "equation of motion" in the phi^4 model
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography