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.

arXiv comment27 pages, 1 figure; v2: published version

References in corpus (29)

• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• The Bootstrap Program for Boundary CFT_d
• The Theory of Boundary Critical Phenomena
• Conformal Field Theories Near a Boundary in General Dimensions
• Bootstrapping the 3d Ising twist defect
• A Mellin space approach to the conformal bootstrap
• Conformal Bootstrap in Mellin Space
• Boundary and Interface CFTs from the Conformal Bootstrap
• Energy Momentum Tensor in Conformal Field Theories Near a Boundary
• Localized magnetic field in the $O(N)$ model
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Line and surface defects for the free scalar field
• Analytic Bootstrap for Boundary CFT
• CFT in AdS and boundary RG flows
• Generalized Wilson-Fisher critical points from the conformal OPE
• On critical exponents without Feynman diagrams
• Bootstrapping line defects with $O(2)$ global symmetry
• $\epsilon$-Expansion in the Gross-Neveu Model from Conformal Field Theory
• Classical equation of motion and Anomalous dimensions at leading order
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• 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
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• On Analytic Bootstrap for Interface and Boundary CFT
• $\epsilon$-Expansion in the Gross-Neveu CFT
• 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