  Warped string compactifications are central to many attempts to stabilize
moduli and connect string theory with cosmology and particle phenomenology. We
present a first-principles derivation of the low-energy 4D effective theory
from dimensional reduction of a D3-brane in a warped Calabi-Yau
compactification of type IIB string theory with imaginary self-dual 3-form
flux, including effects of D3-brane motion beyond the probe approximation, and
find the metric on the moduli space of brane positions, the universal volume
modulus, and axions descending from the 4-form potential. As D3-branes may be
considered as carrying either electric or magnetic charges for the self-dual
5-form field strength, we present calculations in both duality frames. Our
results are consistent with, but extend significantly, earlier results on the
low-energy effective theory arising from D3-branes in string compactifications.
