On Conifolds and D3-branes

TL;DR

This paper investigates Ricci-flat, Kähler geometries asymptotic to the T^{11} cone, exploring their singularities and the effects of D3-branes, including solutions with horizons and divergent mass.

Contribution

It provides new explicit solutions for Ricci-flat, Kähler geometries related to T^{11} and analyzes their singularities and supersymmetric D3-brane configurations.

Findings

Metrics are singular in the interior with no regular horizons.

Introducing D3-branes does not produce regular black hole horizons.

A supersymmetric ansatz yields solutions with horizons and logarithmically divergent mass.

Abstract

We search for Ricci flat, K\"{a}hler 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^{11}. 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.