Inverting geometric transitions: explicit Calabi-Yau metrics for the Maldacena-Nunez solutions

Abstract

Explicit Calabi-Yau metrics are derived that are argued to map to the Maldacena-Nu\~{n}ez AdS solutions of M-theory and IIB under geometric transitions. In each case the metrics are singular where a H^2 K\"{a}hler two-cycle degenerates but are otherwise smooth. They are derived as the most general Calabi-Yau solutions of an ansatz for the supergravity description of branes wrapped on K\"{a}hler two-cycles. The ansatz is inspired by re-writing the AdS solutions, and the structure defined by half their Killing spinors, in this form. The world-volume theories of fractional branes wrapped at the singularities of these metrics are proposed as the duals of the AdS solutions. The existence of supergravity solutions interpolating between the $AdS$ and Calabi-Yau metrics is conjectured and their boundary conditions briefly discussed.