On Conifolds and D3-branes

We search for Ricci flat, Kähler geometries which are asymptotic to the cone whose base is the space T 11 by working out covariantly constant spinor equations. The metrics we find are singular in the interior and introducing parallel D3-branes does not form regular event horizons cloaking the naked singularities. We also work out a supersymmetric ansatz involving only the metric and the 5-form field corresponding to D3-branes wrapping over the non-trivial 2-cycle of T . We find a system of first-order equations and argue that the solution has an event horizon and the ADM mass per unit volume diverges logarithmically. [email protected] The conifold is a 6-dimensional complex manifold described by a quadric equation in C z 1 + z 2 2 + z 2 3 + z 2 4 = 0. (1) It can be shown that this quadric is a cone whose base is S × S. It is also possible to find a Ricci flat, Kähler metric on the conifold [1], which may be written as ds = dr + r2ds2T 11 , (2) where the Einstein space T 11 has the topology S × S. The Einstein metric of T 11 can be written explicitly