Functional perturbative RG and CFT data in the $\epsilon$-expansion

Abstract

We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the $\epsilon$-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multicritical models ${\varphi }^{2n}$. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks.

39 pages, 3 figures; v3: matches published version

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• Functional Renormalization and $\overline{\text{MS}}$
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Leading order CFT analysis of multi-scalar theories in d>2
• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• Scaling solutions in the derivative expansion
• In search of a UV completion of the Standard Model - 378.000 models that don't work
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• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• Platonic Field Theories
• Multi-critical multi-field models: a CFT approach to the leading order
• Scheme dependence of asymptotically free solutions
• Exact solutions and residual regulator dependence in functional renormalisation group flows
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Renormalization of multicritical scalar models in curved space
• Conformal Data of Fundamental Gauge-Yukawa Theories
• The tricritical Ising CFT and conformal bootstrap
• Anomalous Dimensions in Hypercubic 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
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Operator product expansion coefficients from the nonperturbative functional renormalization group