Supersymmetric probes on the conifold

TL;DR

This paper investigates supersymmetric D-brane embeddings in the AdS_5 x T^{1,1} geometry, identifying stable configurations and their dual gauge theories using kappa symmetry.

Contribution

It provides a comprehensive analysis of supersymmetric D3, D5, and D7-brane embeddings in the conifold background, including new stable and supersymmetric configurations.

Findings

Identified supersymmetric three-cycles for D3-branes.

Determined gauge theory duals of these embeddings.

Found stable non-supersymmetric configurations.

Abstract

We study the supersymmetric embeddings of different D-brane probes in the AdS_5 x T^{1,1} geometry. The main tool employed is kappa symmetry and the cases studied include D3-, D5- and D7-branes. We find a family of three-cycles of the T^{1,1} space over which a D3-brane can be wrapped supersymmetrically and we determine the field content of the corresponding gauge theory duals. Supersymmetric configurations of D5-branes wrapping a two-cycle and of spacetime filling D7-branes are also found. The configurations in which the entire T^{1,1} space is wrapped by a D5-brane (baryon vertex) and a D7-brane are also studied. Some other embeddings which break supersymmetry but are nevertheless stable are also determined.