We consider the effect of warping on the distribution of type IIB flux vacua constructed with Calabi-Yau orientifolds. We derive an analytical form of the distribution that incorporates warping and find close agreement with the results of a Monte Car
lo enumeration of vacua. Compared with calculations that neglect warping, we find that for any finite volume compactification, the density of vacua is highly diluted in close proximity to the conifold point, with a steep drop-off within a critical distance.
We investigate flux vacua on a variety of one-parameter Calabi-Yau compactifications, and find many examples that are connected through continuous monodromy transformations. For these, we undertake a detailed analysis of the tunneling dynamics and fi
nd that tunneling trajectories typically graze the conifold point---particular 3-cycles are forced to contract during such vacuum transitions. Physically, these transitions arise from the competing effects of minimizing the energy for brane nucleation (facilitating a change in flux), versus the energy cost associated with dynamical changes in the periods of certain Calabi-Yau 3-cycles. We find that tunneling only occurs when warping due to back-reaction from the flux through the shrinking cycle is properly taken into account.
