Comments on epsilon expansion of the O$(N)$ model with boundary

Abstract

The O$(N)$ vector model in the presence of a boundary has a non-trivial fixed point in $(4-\epsilon )$ dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is investigated at the leading order in the $\epsilon$-expansion by diagrammatic and axiomatic approaches. In the latter, we extend the framework of Rychkov and Tan for the bulk theory to the case with a boundary and calculate the conformal dimensions of boundary composite operators with attention to the analyticity of correlation functions. In both approaches, we obtain consistent results.

27 pages, 1 figure; v2: published version

References in corpus (9)

• Conformal Bootstrap in Mellin Space
• Localized magnetic field in the $O(N)$ model
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Generalized Wilson-Fisher critical points from the conformal OPE
• Bootstrapping line defects with $O(2)$ global symmetry
• Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• The $\epsilon$-expansion of the codimension two twist defect from conformal field theory

Cited by in corpus (6)

• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• Analytic bootstrap for magnetic impurities
• The O(N)-flavoured replica twist defect
• 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