Resolved Calabi-Yau cones and flows from Labc superconformal field theories

We discuss D3-branes on cohomogeneity-three resolved Calabi-Yau cones over L-abc spaces, for which a 2-cycle or 4-cycle has been blown up. In terms of the dual quiver gauge theory, this corresponds to motion along the non-mesonic, or baryonic, directions in the moduli space of vacua. In particular, a dimension-two and/or dimension-six scalar operator gets a vacuum expectation value. These resolved cones support various harmonic (2, 1)-forms which reduce the ranks of some of the gauge groups either by a Seiberg duality cascade or by Higgsing. We also discuss higher-dimensional resolved Calabi-Yau cones. In particular, we obtain square-integrable (2, 2)-forms for eight-dimensional cohomogeneity-four Calabi-Yau metrics. Published by Elsevier B.V.