  We study the dynamics of a D3 brane in generic IIB warped compactifications,
using the Hamiltonian formulation discussed in arXiv:0805.3700 [hep-th]. Taking
into account of both closed and open string fluctuations, we derive the warped
Kahler potential governing the motion of a probe D3 brane. By including the
backreaction of D3, we also comment on how the problem of defining a
holomorphic gauge coupling on wrapped D7 branes in warped background can be
resolved.
