Line Defect RG Flows in the $\epsilon$ Expansion

Abstract

A general analysis of line defect renormalisation group (RG) flows in the $\epsilon$ expansion below $d=4$ dimensions is undertaken. The defect beta function for general scalar-fermion bulk theories is computed to next-to-leading order in the bulk couplings. Scalar models as well as scalar-fermion models with various global symmetries in the bulk are considered at leading non-trivial order. Different types of potential infrared (IR) defect conformal field theories (dCFTs) and their RG stability are discussed. The possibility of multiple IR stable dCFTs is realised in specific examples with hypertetrahedral symmetry in the bulk. The one-point function coefficient of the order parameter in the stable IR dCFT of the cubic model is computed at next-to-leading order and compared with that in the IR dCFT of the Heisenberg model.

30 pages, 3 figures. v2 added clarifying comments and citations. v3 added further comments, to be published in JHEP

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Cited by in corpus (8)

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• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Analytic bootstrap for magnetic impurities
• Defects, Rigid Holography and $C$-theorems
• Conformal line defects at finite temperature
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Fine Spectrum from Crude Analytic Bootstrap
• Note on surface defects in multiscalar critical models