Master Space, Hilbert Series and Seiberg Duality

TL;DR

This paper studies how Seiberg duality affects the combined mesonic and baryonic moduli space of quiver gauge theories from D3 branes at Calabi-Yau singularities, focusing on the structure of the master space and Hilbert Series.

Contribution

It demonstrates that the Hilbert Series of the largest component of the master space remains invariant across different toric phases when refined with all non anomalous charges, linking phases via Seiberg duality.

Findings

Hilbert Series is the same for different phases when refined properly.

Seiberg duality relates different toric phases of the same singularity.

Master space structure is consistent across phases for multiple branes.

Abstract

We analyze the action of Toric (Seiberg) duality on the combined mesonic and baryonic moduli space of quiver gauge theories obtained from D3 branes at Calabi-Yau singularities. We analyze in particular the structure of the master space, the complete moduli space for one brane, for different toric phases of a given singularity. We show that the Hilbert Series for the largest component of the master space of different phases is the same, when refined with all the non anomalous charges. This reflects the fact that the quiver gauge theories associated with different phases are related by Seiberg duality when the number of branes is greater than one.