  We give a comprehensive treatment of the scalar potential for a D3-brane in a
warped conifold region of a compactification with stabilized moduli. By
studying general ultraviolet perturbations in supergravity, we systematically
incorporate `compactification effects' sourced by supersymmetry breaking in the
compact space. Significant contributions to the D3-brane potential, including
the leading term in the infrared, arise from imaginary anti-self-dual (IASD)
fluxes. For an arbitrary Calabi-Yau cone, we determine the most general IASD
fluxes in terms of scalar harmonics, then compute the resulting D3-brane
potential. Specializing to the conifold, we identify the operator dual to each
mode of flux, and for chiral operators we confirm that the potential computed
in the gauge theory matches the gravity result. The effects of four-dimensional
curvature, including the leading D3-brane mass term, arise directly from the
ten-dimensional equations of motion. Furthermore, we show that gaugino
condensation on D7-branes provides a local source for IASD flux. This flux
precisely encodes the nonperturbative contributions to the D3-brane potential,
yielding a promising ten-dimensional representation of four-dimensional
nonperturbative effects. Our result encompasses all significant contributions
to the D3-brane potential discussed in the literature, and does so in the
single coherent framework of ten-dimensional supergravity. Moreover, we
identify new terms with irrational scaling dimensions that were inaccessible in
prior works. By decoupling gravity in a noncompact configuration, then
systematically reincorporating compactification effects as ultraviolet
perturbations, we have provided an approach in which Planck-suppressed
contributions to the D3-brane effective action can be computed.
