Supersymmetric Branes on AdS_5 x Y^{p,q} and their Field Theory Duals

TL;DR

This work classifies supersymmetric brane embeddings in $AdS_5\times Y^{p,q}$ using kappa symmetry, revealing D3-brane dibaryons on singlet and doublet three-cycles, a new family of embeddings, and their BPS fluctuations that match the dual quiver operators. It also identifies D5-domain-wall configurations, explores flux-enabled and non-SUSY stable branes, and analyzes spacetime-filling D7-branes as flavor branes with holomorphic embedding structure, including a comprehensive calibration and energy-bounds framework. The results solidify the AdS/CFT dictionary for $Y^{p,q}$ theories, connecting geometric cycles to dibaryons, mesons, domain walls, and flavor sectors, while highlighting global-topology issues and open questions about wrapped-brane spectra and holographic K-theory. Overall, the paper enhances understanding of how brane probes encode protected operator data and nonperturbative features in $Y^{p,q}$ quiver gauge theories, with broader implications for Sasaki-Einstein holography.

Abstract

We systematically study supersymmetric embeddings of D-brane probes of different dimensionality in the AdS_5xY^{p,q} background of type IIB string theory. The main technique employed is the kappa symmetry of the probe's worldvolume theory. In the case of D3-branes, we recover the known three-cycles dual to the dibaryonic operators of the gauge theory and we also find a new family of supersymmetric embeddings. The BPS fluctuations of dibaryons are analyzed and shown to match the gauge theory results. Supersymmetric configurations of D5-branes, representing domain walls, and of spacetime filling D7-branes (which can be used to add flavor) are also found. We also study the baryon vertex and some other embeddings which break supersymmetry but are nevertheless stable.

Figures (2)

• Figure 1: The basic cells $\sigma$ (upper left) and $\tau$ (upper right). $Y^{p,q}$ quivers are built with $q$$\sigma$ and $p-q$$\tau$ unit cells. The cubic terms in the superpotential (\ref{['supYpq']}) come from closed loops of the former and the quartic term arises from the latter. The quiver for $Y^{4,2}$ is given by $\sigma\tilde{\sigma}\tau\tilde{\tau}$ (bottom).
• Figure 2: Loops in the $Y^{4,2}$ quiver representing mesonic operators in the chiral ring. There are short loops such as $UVY$, $VUY$ or $YUZU$ (upper), longest loops as $VUVUZUZU$ (middle) and long loops like $YUYYYU$ (bottom). The representative of each class in the chiral ring is, respectively, ${\cal O}_1$, ${\cal O}_2$ and ${\cal O}_3$.