By E. Palti
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Extra resources for Aspects of Moduli Stabilization in String and M-Theory [thesis]
Before we proceed with that it is interesting, although somewhat speculative, to consider the physical interpretation of the resolution of the conifold singularity by quantum string theory. A topology change of spacetime requires the fabric of space-time to be somehow ’ripped’ and ’glued’ back together. It seems that string theory allows such a process without breaking down. A possible explanation for this might come from the fact that string theory can only probe scales down to the self-dual scale.
15) ˜ sk = 0 and so A covariantly holomorphic section of the U (1) bundle is defined as ∇a¯ Ω ˜ sk = e 12 K sk Ωsk covariantly holomorphic sections of the U (1) flow into under the map Ω holomorphic sections of L. 16) ∇a¯ Ωsk = ∂a¯ Ωsk = 0 . 17) This gives the covariant derivative, with respect to K¨ ahler transformations, acting on Ωsk . Supersymmetry implies that the vectors in the vector multiplet sector should follow the same geometry as the scalars and indeed this is the case. In fact this relation between the vectors and the scalars is the important constraint through which the whole geometric structure is derived.
The Moduli Trapping and Conifold Transitions in Type IIB String Theory 44 study of five-dimensional cosmology associated with a flop of the internal space in Mtheory was initiated in  and followed up in [44,45]. There it was found that the tension of any M2-branes wrapping the collapsing two-cycles caused the cycles to remain small, so the moduli forced the CY to remain near the flop point. This ruled out a dynamical realisation of a flop transition. In the conifold transition, which we study here, a three-cycle on one side of the transition collapses and then re-expands into a two-cycle, thus changing the Hodge numbers of the CY.