Branes on a tip of a conifold; how to understand it? I am not sure if this question makes sense "intuitively" but here it is. In Klebanov-Witten theory one puts branes on the tip of a cone over a Calabi-Yau manifold. My question is what does it mean to put a "D-brane on a tip" which is a singularity? I cannot understand where this tip is spatially located. Nor can I understand if the cone breaks or not Lorentz symmetry in the 10d space.
 A: It might help to think of obtaining Klebanov-Witten theory in a limiting proceedure. Imagine a dynamical setting where the branes don't start out at the singularity, but instead at some smooth point near the singularity. Then move them to the conifold point. And the conifold point can be located because it's a singular point. If we choose coordinates so that the conifold is at $r=0$, then the metric is
$ds^2 = dr^2 + r^2 ds^2(T^{1,1}),$ 
which is a cone. Because the second factor isn't a round sphere with unit radius, this has a curvature singularity at $r=0$. The conifold is also often described as the quartic in $\mathbb{C}^4$: $\sum_{i=1}^4 (z^i)^2 = 0$.
The cone doesn't affect the Lorentz symmetry of the Minkowski space. The metric for the full 10D solution looks like 
$ds^2 = H^{-1/2} dx_{\mu}dx^{\mu} +  H^{1/2} ds_6^2$,
where in the usual case $ds_6^2 = ds^2(\mathbb{R}^6)$. In Klebanov-Witten (or Klebanov-Tseytlin) it is the space written above with the $\mathbb{T}^{1,1}$ factor.
By the way, the singularity of the conifold in the Klebanov-Tseytlin solution get's ``fixed'' by replacing the conifold with the deformed conifold in Klebanov-Strassler.
