We use holography to study the spectra of boundary conformal field theories
(BCFTs). To do so, we consider a 2-dimensional Euclidean BCFT with two circular
boundaries that correspond to dynamical end-of-the-world branes in
3-dimensional gravity. Interactions between these branes inform the operator
content and the energy spectrum of the dual BCFT. As a proof of concept, we
first consider two highly separated branes whose only interaction is taken to
be mediated by a scalar field. The holographic computation of the
scalar-mediated exchange reproduces a light scalar primary and its global
descendants in the closed-string channel of the dual BCFT. We then consider a
gravity model with point particles. Here, the interaction of two separated
branes corresponds to a heavy closed-string operator which lies below the black
hole threshold. However, we may also consider branes at finite separation that
“merge” non-smoothly. Such brane mergers can be used to describe unitary
sub-threshold boundary-condition-changing operators in the open-string spectrum
of the BCFT. We also find a new class of sub-threshold Euclidean bra-ket
wormhole saddles with a factorization puzzle for closed-string amplitudes.
