  We study Fateev-Zamolodchikov-Zamolodchikov-Teschner (FZZT) branes in
Witten-Kontsevich topological gravity, which includes Jackiw-Teitelboim (JT)
gravity as a special case. Adding FZZT branes to topological gravity
corresponds to inserting determinant operators in the dual matrix integral and
amounts to a certain shift of the infinitely many couplings of topological
gravity. We clarify the perturbative interpretation of adding FZZT branes in
the genus expansion of topological gravity in terms of a simple boundary factor
and the generalized Weil-Petersson volumes. As a concrete illustration we study
JT gravity in the presence of FZZT branes and discuss its relation to the
deformations of the dilaton potential that give rise to conical defects. We
then construct a non-perturbative formulation of FZZT branes and derive a
closed expression for the general correlation function of multiple FZZT branes
and multiple macroscopic loops. As an application we study the FZZT-macroscopic
loop correlators in the Airy case. We observe numerically a void in the
eigenvalue density due to the eigenvalue repulsion induced by FZZT-branes and
also the oscillatory behavior of the spectral form factor which is expected
from the picture of eigenbranes.
