Geometric transitions, flops and non-Kähler manifolds: I

Abstract

We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G 2 manifolds that are circle fibrations over non-Kähler manifolds is presented.Contents 1 Notice that this term also plays a crucial role in the S-duality conjecture of [5].2 The manifold that we will eventually get in type IIA side later in this paper, will however be more general than the half-flat manifold in the sense that both dΩ ± = 0.3 The outcome of these T-dualities is different from the ones of [21],[22] and [23] where one T-duality takes a type IIB picture to a type IIA brane configuration. 4 There have been previous attempts to relate the resolved conifold and the deformed conifold by starting with the deformed conifold [24]. As the deformed conifold does not admit a T 3fibration using this manifold as a starting point may seem more problematic, although, we have been informed that there are some papers that overcome this problem [25].

Lumps in the throat

“…(c) For the warped resolved conifold case, the F-theory lift has been shown to exist in the third reference of [38]. In fact a conifold transition can be shown to reproduce the F-theory lift of the deformed case also.…”

“…The original Klebanov-Strassler model [21] has a similar structure at the far IR of the geometry, but differs from our case by the absence of three and seven branes. The geometry that is closest to our set-up is the one that was studied in [38] (for short reviews see [39]). We will soon provide a more rigorous way to analyse these coefficients (which was not attempted before).…”

“…The next question therefore is to ask whether the U(1) dz-fibration would change or not. Here we can take a cue from the Klebanov-Strassler solution [21] and the geometrical transition set-up of [38]. The U(1) fibrations in both set-ups remain the same.…”

“…This is also exactly the regime where in [43] the analysis of uplifting was done. The mass of the string stretched between the three and seven branes is therefore 38) with m AB computed using the line element for (dr, dx) using a warped conifold 14 . Our constraint therefore is that m computed using the metric should be minimised.…”

Dipole-deformed bound states and heterotic Kodaira surfaces

“…The conformally Kähler geometry we studied in our earlier works [17], [21], [16], [18] exhibits a globally integrable complex structure derived from an F-theory picture. As such, both bi-fundamental and fundamental matter appeared in the construction due to the presence of three, five and seven-branes.…”