Dibaryons from Exceptional Collections

TL;DR

The paper establishes a precise dictionary between dibaryons in N=1 quiver gauge theories at del Pezzo cones and D3-branes wrapped on holomorphic curves in the dual geometry, achieved via a dual exceptional collection on the del Pezzo surface. Dibaryon charges and R-symmetries are read off from divisors and their intersections, with tr R Q_I Q_J identified with geometric intersection forms; a-maximization and NSVZ constraints fix R-charges, and Markov-type Diophantine relations organize three-block quivers. The approach yields broad consistency checks across many del Pezzo surfaces, including explicit, fully worked three-block and higher-block examples, and provides a framework to study non-conformal deformations and Seiberg dualities as mutations of the dual collection. The results offer a robust, Weyl-group-ambiguity-free method to match gauge-theory dibaryons with geometric cycles, with potential applications to generalized conifolds and non-toric geometries. Overall, the work deepens the geometric understanding of holographic dibaryons and links quiver anomalies, divisor arithmetic, and exceptional collections in a unified formalism.

Abstract

We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription identifies the R-charge R and all baryonic U(1) charges Q_I with divisors in the del Pezzo surface without any Weyl group ambiguity. As one application of the correspondence, we identify the cubic anomaly tr R Q_I Q_J as an intersection product for dibaryon charges in large-N superconformal gauge theories. Examples can be given for all del Pezzo surfaces using three- and four-block exceptional collections. Markov-type equations enforce consistency among anomaly equations for three-block collections.

Figures (7)

• Figure 1: Quiver for ${\mathbb P}^2$.
• Figure 2: Examples of subquivers that can be used to construct dibaryon operators in the field theory.
• Figure 3: Quivers for a) $\mathbb{P}^{1} \times \mathbb{P}^{1}$ and b) $\mathbb{P}^{2}$ blown up at a point.
• Figure 4: Quiver for the second del Pezzo.
• Figure 5: Quiver for a three-block exceptional collection.