Notes on a Surface Defect in the $O(N)$ Model

Abstract

We study a surface defect in the free and critical $O(N)$ vector models, defined by adding a quadratic perturbation localized on a two-dimensional subspace of the $d$-dimensional CFT. We compute the beta function for the corresponding defect renormalization group (RG) flow, and provide evidence that at long distances the system flows to a nontrivial defect conformal field theory (DCFT). We use epsilon and large $N$ expansions to compute several physical quantities in the DCFT, finding agreement across different expansion methods. We also compute the defect free energy, and check consistency with the so-called $b$-theorem for RG flows on surface defects.

arXiv comment39 pages. v2: various improvements, references added

References in corpus (20)

• AdS/CFT Correspondence and Symmetry Breaking
• The Bootstrap Program for Boundary CFT_d
• The Theory of Boundary Critical Phenomena
• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature
• F-Theorem without Supersymmetry
• A universal result on central charges in the presence of double-trace deformations
• Quantum criticality under decoherence or weak measurement
• A Constraint on Defect and Boundary Renormalization Group Flows
• Partition functions and double-trace deformations in AdS/CFT
• Towards a $C$-theorem in defect CFT
• Localized magnetic field in the $O(N)$ model
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• CFT in AdS and boundary RG flows
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Critical behavior in the presence of an order-parameter pinning field
• Defects in scalar field theories, RG flows and Dimensional Disentangling
• XY* transition and extraordinary boundary criticality from fractional exciton condensation in quantum Hall bilayer
• RG Flows and Stability in Defect Field Theories

Cited by in corpus (12)

• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Analytic bootstrap for magnetic impurities
• Boundary and defect criticality in topological insulators and superconductors
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
• Rényi Entropy with Surface Defects in Six Dimensions
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Holographic dual of defect CFT with corner contributions
• Fine Spectrum from Crude Analytic Bootstrap
• Note on surface defects in multiscalar critical models
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
• Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter