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.

58 pages, 5 figures; v2: references added

References in corpus (7)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Boundary Conformal Field Theory and a Boundary Central Charge
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• 3d Abelian Gauge Theories at the Boundary

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• Casimir Forces in CFT with Defects and Boundaries
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• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Spontaneous symmetry breaking in free theories with boundary potentials
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• 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