Boundaries in free higher derivative conformal field theories

Abstract

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.

Analytic and numerical bootstrap for the long-range Ising model

“…In the case of unitary and local BCFTs,[30] proved that a vector of dimension d is absent from the spectrum of boundary primaries. One can find counter-examples when unitarity is given up[80]. Via the same reasoning, one can prove that for unitary and local p-dimensional conformal defects a vector of dimension p + 1 should be absent from the spectrum of defect primaries.…”