Bootstrapping boundary-localized interactions II: Minimal models at the boundary

Abstract

We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can demonstrate the existence of the fixed point perturbatively, and for smaller values we use the numerical conformal bootstrap to obtain a sharp kink that smoothly matches onto the perturbative predictions. The wider numerical analysis also yields universal bounds for the spectrum of any other boundary condition for the free scalar field. A second kink in these bounds hints at a second class of non-standard boundary conditions, as yet unidentified.

45 pages, 10 figures; v2: published version

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• Casimir Forces in CFT with Defects and Boundaries
• Conformal boundary conditions for a 4d scalar field
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Boundary and defect criticality in topological insulators and superconductors
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