Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories

Abstract

In the free ${\square }^k$ scalar conformal field theory, there exist conserved and partially-conserved higher-spin currents. We study their anomalous dimensions associated with ${\varphi }^{2n}$ interaction in the $\epsilon$ expansion. We derive general formulae for the leading corrections from the conformal multiplet recombination, and verify their consistency with crossing symmetry using the Lorentzian inversion formula. The results are further extended to the O($N$) models.

v3: 34 pages, 4 figures, discussion improved, references added, typos corrected; v2: discussion about the N dependence of Chew-Frautschi plot added, Fig.3 and Fig. 4 added, typos corrected, minor improvements, notation simplified, references updated

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• Principle of minimal singularity for Green's functions
• The tricritical Ising CFT and conformal bootstrap
• Coupled minimal models revisited II: Constraints from permutation symmetry
• ${\varphi }^n$ trajectory bootstrap
• 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