Boundaries in Free Higher Derivative Conformal Field Theories

TL;DR

Addresses BCFTs for free higher-derivative scalars and fermions, proposing a systematic method to identify conformal boundary conditions by removing boundary primaries. It uncovers a rich network of RG flows between boundary conditions driven by quadratic deformations, and computes hemisphere free energy and displacement-operator correlators, revealing violations of the boundary a-theorem due to bulk non-unitarity. The work provides explicit constructions of boundary primaries, a detailed analysis of BCs for scalar and fermion higher-derivative theories, and a duality between conjugate boundary conditions. These results illuminate non-unitary BCFTs and offer a framework for exploring higher-derivative boundary physics and potential holographic connections.

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.

Figures (2)

• Figure 1: Some of the boundary RG flows induced in the $k=2$ system (left) and $k=3$ system (right). There are additional flows, not shown, along the diagonals of the square and the diagonals of the faces of the hypercube, induced by $c\space \Phi^{(k,q)} \Phi^{(k,q')}$, $q \neq q'$, type deformations.
• Figure 2: The RG flows triggered by relevant boundary deformations in the $\slashed{\partial}^3 \psi$ theory.