Dibaryons from Exceptional Collections

TL;DR

This paper explores the correspondence between brane configurations in del Pezzo geometries and dibaryons in dual superconformal quiver gauge theories, providing a geometric method to determine charges and anomalies.

Contribution

It introduces a K-theoretic approach using exceptional collections to identify dibaryon spectra and charges without Weyl ambiguity, linking geometric divisors to gauge theory anomalies.

Findings

Identifies R and baryonic charges with divisors in del Pezzo surfaces.

Provides a geometric interpretation of the cubic anomaly as an intersection product.

Demonstrates the approach with examples for all del Pezzo surfaces.

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.