Anomalous dimensions of spinning operators from conformal symmetry

Abstract

We compute, to the first non-trivial order in the $\epsilon$-expansion of a perturbed scalar field theory, the anomalous dimensions of an infinite class of primary operators with arbitrary spin $\ell =0,1,..$, including as a particular case the weakly broken higher-spin currents, using only constraints from conformal symmetry. Following the bootstrap philosophy, no reference is made to any Lagrangian, equations of motion or coupling constants. Even the space dimensions d are left free. The interaction is implicitly turned on through the local operators by letting them acquire anomalous dimensions. When matching certain four-point and five-point functions with the corresponding quantities of the free field theory in the $\epsilon \to 0$ limit, no free parameter remains. It turns out that only the expected discrete d values are permitted and the ensuing anomalous dimensions reproduce known results for the weakly broken higher-spin currents and provide new results for the other spinning operators.

20 pages.v2: an important remark and references added, more examples included

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Cited by in corpus (12)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Universality at large transverse spin in defect CFT
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Applications of dispersive sum rules: $\epsilon$-expansion and holography
• A Basis of Analytic Functionals for CFTs in General Dimension
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Thermal CFTs in momentum space
• Bounds on multiscalar CFTs in the epsilon expansion
• The tricritical Ising CFT and conformal bootstrap
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations