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

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