Dimensional Reduction for D3-brane Moduli
  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. 
Brad Cownden, Andrew R. Frey, M. C. David Marsh, and Bret Underwood
hep-th