The information metric on the space of boundary coupling constants in
two-dimensional conformal field theories is studied. Such a metric is related
to the Casimir energy difference of the theory defined on an interval. We
concretely compute the information metric on the boundary conformal manifold of
free boson CFT as well as SU(2)k WZW theory, obtaining the result expected from
the symmetry of the systems. We also compute the information metric on the
space of non-conformal boundary states produced by boundary mass perturbations
in the theory of a real free scalar. The holographic dual of the boundary
information metric in the context of AdS3/BCFT2 is also discussed. We argue
that it corresponds to the area of the minimal cross section of the
end-of-the-world brane connecting two boundaries of the asymptotic BCFTs.Comment: 31 page