Bootstrapping boundary-localized interactions

Abstract

We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a `shadow pair' of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a `kink' in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

arXiv comment58 pages, 5 figures; v2: references added

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Cited by in corpus (32)

• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Line and surface defects for the free scalar field
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Bootstrapping line defects with $O(2)$ global symmetry
• New Developments in the Numerical Conformal Bootstrap
• Defect $a$-Theorem and $a$-Maximization
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Analytic bootstrap for the localized magnetic field
• On Analytic Bootstrap for Interface and Boundary CFT
• A dispersion relation for defect CFT
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Conformal dispersion relations for defects and boundaries
• Two Point Functions in Defect CFTs
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
• Conformal Bootstrap near the edge
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Analytic and numerical bootstrap for the long-range Ising model
• Fusion of conformal defects in four dimensions
• Renormalization group flows in AdS and the bootstrap program
• Defect Conformal Blocks from Appell Functions
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• Universal Spinning Casimir Equations and Their Solutions
• Casimir Forces in CFT with Defects and Boundaries
• Conformal boundary conditions for a 4d scalar field
• The ordinary surface universality class of the three-dimensional O($N$) model
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Spontaneous symmetry breaking in free theories with boundary potentials
• 3d Large $N$ Vector Models at the Boundary
• Note on surface defects in multiscalar critical models
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations