  In this paper, we investigate AdS/BCFT for curvature-squared gravity. To warm
up, we start with Gauss-Bonnet gravity. We derive the one point function of
stress tensor and show that the central charge related to the norm of
displacement operator is positive for the couplings obeying causality
constraints. Furthermore, by imposing the null energy condition on the
end-of-the-world brane, we prove the holographic g-theorem for Gauss-Bonnet
gravity. This corrects a wrong point of view in the literature, which claims
that the holographic g-theorem is violated for Gauss-Bonnet gravity. As a
by-product, we obtain the boundary entropy and A-type boundary central charges
in general dimensions. We also study AdS/BCFT for general curvature-squared
gravity. We find that it is too restrictive for the shape of the brane and the
dual BCFT is trivial if one imposes Neumann boundary conditions for all of the
gravitational modes. Instead, we propose to impose Dirichlet boundary condition
for the massive graviton, while imposing Neumann boundary condition for the
massless graviton. In this way, we obtain non-trivial shape dependence of
stress tensor and well-defined central charges. In particular, the holographic
g-theorem is satisfied by general curvature-squared gravity. Finally, we
discuss the island and show that the Page curve can be recovered for
Gauss-Bonnet gravity. Interestingly, there are zeroth-order phase transitions
for the Page curve within one range of couplings obeying causality constraints.
Generalizing the discussions to holographic entanglement entropy and
holographic complexity in AdS/CFT, we get new constraints for the Gauss-Bonnet
coupling, which is stronger than the causality constraint.
