Resolved Calabi-Yau Cones and Flows from L^{abc} Superconformal Field Theories

TL;DR

This paper studies D3-branes on resolved Calabi-Yau cones over L^{abc} spaces, linking geometric resolutions to baryonic directions in dual gauge theories and exploring harmonic forms and higher-dimensional cases.

Contribution

It introduces new resolved Calabi-Yau cone solutions over L^{abc} spaces and analyzes their dual gauge theory moduli space and harmonic forms, including higher-dimensional cases.

Findings

Resolved cones support harmonic (2,1)-forms affecting gauge group ranks.

Vacuum expectation values of scalar operators correspond to geometric resolutions.

Constructs square-integrable (2,2)-forms for eight-dimensional Calabi-Yau metrics.

Abstract

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.