$\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory

Abstract

We use a compatibility between the conformal symmetry and the equations of motion to solve the one-point function in the critical ${\varphi }^3$-theory (a.k.a the critical Lee-Yang model) on the $d=6-\epsilon$ dimensional real projective space to the first non-trivial order in the $\epsilon$-expansion. It reproduces the conventional perturbation theory and agrees with the numerical conformal bootstrap result.

arXiv comment6 pages, v2: some references added

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Cited by in corpus (28)

• A Mellin space approach to the conformal bootstrap
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
• Lee-Yang model from the functional renormalization group
• Leading CFT constraints on multi-critical models in d>2
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• Crossing Kernels for Boundary and Crosscap CFTs
• Aspects of CFTs on Real Projective Space
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• A dispersion relation for defect CFT
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Inverse Bootstrapping Conformal Field Theories
• Leading order CFT analysis of multi-scalar theories in d>2
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Operator product expansion coefficients in the exact renormalization group formalism
• Three ways to solve critical ${\varphi }^4$ theory on $4-\epsilon$ dimensional real projective space: perturbation, bootstrap, and Schwinger-Dyson equation
• Anomalous dimensions of spinning operators from conformal symmetry
• Multi-critical multi-field models: a CFT approach to the leading order
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Universal Dynamics in Non-Orientable CFT${}_2$
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• From $\mathcal{N}=4$ Super-Yang-Mills on ${\mathbb{RP}}^4$ to bosonic Yang-Mills on ${\mathbb{RP}}^2$
• CFTs on curved spaces
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations