Baryonic Generating Functions

TL;DR

This paper develops a method using the plethystic program to compute baryonic generating functions that count BPS operators in quiver gauge theories, providing exact results for specific geometries and revealing baryonic charge as a quantized Kähler modulus.

Contribution

It introduces a novel application of the plethystic program to baryonic generating functions in quiver gauge theories, solving a longstanding combinatorial problem and linking baryonic charge to geometric moduli.

Findings

Exact expressions for baryonic generating functions in conifold and orbifold theories.

Baryonic charge corresponds to the quantized Kähler modulus of the geometry.

Enables statistical analysis of quiver theories on baryonic branches.

Abstract

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.