$\epsilon$-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.

6 pages, v2: some references added

References in corpus (7)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
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• Anomalous dimensions of leading twist conformal operators
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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• A dispersion relation for defect CFT
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• Inverse Bootstrapping Conformal Field Theories
• Comments on epsilon expansion of the O$(N)$ model with boundary
• 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 ${\mathbb{RP}}^2$
• 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