Supersymmetric probes on the conifold

TL;DR

This paper uses kappa symmetry to classify supersymmetric D-brane probes in the KW background $AdS_5\times T^{1,1}$, deriving explicit first-order BPS equations and solving them for D3, D5, and D7 probes. It reveals a family of D3 embeddings on three-cycles (including the dibaryon-related cases) and identifies D5 two-cycle domain walls and spacetime-filling D7 flavor branes, some wrapping the full $T^{1,1}$. The embeddings satisfy DBI equations and saturate energy bounds, and their dual field theory interpretations (dimensions, baryon numbers, and operator content) are articulated, with holomorphic polynomial descriptions tying the gravity solutions to gauge-theory operators. The results illuminate the holographic realization of dibaryons, domain walls, and dynamical flavors in the Klebanov-Witten model and set groundwork for extensions to nonconformal backgrounds like KS.

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.