The critical O(N) CFT: Methods and conformal data

Abstract

The critical $O(N)$ CFT in spacetime dimensions $2<d<4$ is one of the most important examples of a conformal field theory, with the Ising CFT at $N=1$, $2\le d<4$, as a notable special case. Apart from numerous physical applications, it serves frequently as a concrete testing ground for new approaches and techniques based on conformal symmetry. In the perturbative limits - the $4-\epsilon$ expansion, the large $N$ expansion and the $2+\tilde{\epsilon }$ expansion - a lot of conformal data have been computed over the years. In this report, we give an overview of the critical $O(N)$ CFT, including some methods to study it, and present a large collection of conformal data. The data, extracted from the literature and supplemented by many additional computations of order $\epsilon$ anomalous dimensions, are made available through an ancillary data file.

88+13 pages, many tables, one ancillary data file. v2. Revised version, ancillary data file updated. v3. References updated, typos corrected. v4. Data file updated, typos corrected

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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Detectors in weakly-coupled field theories
• Bootstrapping the 3d Ising Stress Tensor
• Analytic bootstrap for the localized magnetic field
• A dispersion relation for defect CFT
• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• Scale without Conformal Invariance in Dipolar Ferromagnets
• Analytic bootstrap for magnetic impurities
• The thermal bootstrap for the critical O(N) model
• The tricritical Ising CFT and conformal bootstrap
• Physical ageing from generalised time-translation-invariance
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Emergent ${\mathbb{Z}}_2$ symmetry near a CDW multicritical point
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Anomalous Dimensions in Hypercubic Theories
• Sphere free energy of scalar field theories with cubic interactions
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• Classifying irreducible fixed points of five scalar fields in perturbation theory
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Ising Cosmology
• Anomalous dimensions at small spins
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• Critical behavior of isotropic systems with strong dipole-dipole interaction from the functional renormalization group
• On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions
• Low-temperature behavior of the $O(N)$ models below two dimensions
• Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing
• Schrödinger-invariance in the voter model