Complex geometry of conifolds and 5-brane wrapped on 2-sphere
G. Papadopoulos, A.A. Tseytlin

TL;DR
This paper explores complex geometric structures of conifolds and wrapped 5-branes in type II supergravity, constructing explicit forms and demonstrating their supersymmetry preservation, unifying various solutions under a universal framework.
Contribution
It provides explicit constructions of complex, Kähler, and (3,0) forms for conifold and 5-brane solutions, and unifies different supergravity solutions via a single ansatz and superpotential approach.
Findings
Explicit complex structures and forms for conifolds and 5-branes.
Demonstration of supersymmetry preservation in these solutions.
Unified description of various brane solutions through a universal ansatz.
Abstract
We investigate solutions of type II supergravity which have the product R^4 x M^6 structure with non-compact M^6 factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N=1 supersymmetric NS5-brane wrapped on 2-sphere solution recently discussed in hep-th/0008001. In all of these cases, we explicitly construct the complex structures, and the Kaehler and parallel (3,0) forms of the corresponding M^6. In addition, we verify that the above solutions preserve, respectively, eight and four supersymmetries of type II theory. We also demonstrate that the ordinary and fractional D3-brane solutions on singular, resolved and deformed conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as special cases from a universal ansatz for the supergravity fields and a single 1-d action governing their radial evolution. We show…
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