Note on surface defects in multiscalar critical models

Abstract

This paper studies generic surface defects for multiscalar critical models using a perturbative $\epsilon$ expansion in $4-\epsilon$ dimensions. The beta functions of the defect couplings for a generic multiscalar bulk with quartic interactions are computed at first non-trivial order in $\epsilon$. Specific bulks of interest are then considered: $O(N)$, hypercubic, hypertetrahdral, and biconical $O(m)\times O(n)$. In each case, we compute fixed points for the defect couplings and determine the remaining bulk symmetry. Expanding beyond the $O(N)$ model, we find a greater variety of patterns of symmetry breaking.

15 pages, 1 figure, 2 tables, v2:references added, v3: corrections in section 3.5, matches published version

References in corpus (19)

• Critical Phenomena and Renormalization-Group Theory
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Quantum Field Theory in the Large N Limit: a review
• Bootstrapping the O(N) Vector Models
• The Theory of Boundary Critical Phenomena
• Boundary and Interface CFTs from the Conformal Bootstrap
• Defects in conformal field theory
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• Bootstrapping boundary-localized interactions
• Notes on a Surface Defect in the $O(N)$ Model
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• On Analytic Bootstrap for Interface and Boundary CFT
• A plane defect in the 3d O$(N)$ model
• Line Defect RG Flows in the $\epsilon$ Expansion
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion

Cited by in corpus (1)

• Fine Spectrum from Crude Analytic Bootstrap