We consider free higher derivative theories of scalars and Dirac fermions in
the presence of a boundary in general dimension. We establish a method for
finding consistent conformal boundary conditions in these theories by removing
certain boundary primaries from the spectrum. A rich set of renormalization
group flows between various conformal boundary conditions is revealed,
triggered by deformations quadratic in the boundary primaries. We compute the
free energy of these theories on a hemisphere, and show that the boundary
a-theorem is generally violated along boundary flows as a consequence of bulk
non-unitarity. We further characterize the boundary theory by computing the
two-point function of the displacement operator.Comment: 49 pages, 2 figures. v2: References and minor comments added. v3:
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