Phases of unstable conifolds

We explore the phase structure induced by closed string tachyon condensation of toric nonsupersymmetric conifold-like singularities described by an integral charge matrix Q = (n1 n2 − n3 − n4), ni > 0, ∑ i Qi 6= 0, initiated in hep-th/0510104. Using gauged linear sigma model renormalization group flows and toric geometry techniques, we see a cascade-like phase structure containing decays to lower order conifold-like singularities, including in particular the supersymmetric conifold and the Y pq spaces. This structure is consistent with the Type II GSO projection obtained previously for these singularities. Transitions between the various phases of these geometries include flips and flops.