On the Master Space for Brane Brick Models

TL;DR

This paper explores the structure of the master space in brane brick models, revealing its algebraic properties and symmetries, which are crucial for understanding 2d (0,2) quiver gauge theories from D1-branes probing toric Calabi-Yau 4-folds.

Contribution

It provides a systematic analysis of the master space for abelian brane brick models, including Hilbert series calculations and symmetry characterizations, advancing the understanding of these gauge theories.

Findings

Hilbert series computed for several examples

Master space generators identified via plethystic programme

Global symmetry representations expressed in Hilbert series

Abstract

We systematically study the master space of brane brick models that represent a large class of 2d (0,2) quiver gauge theories. These 2d (0,2) theories are worldvolume theories of D1-branes that probe singular toric Calabi-Yau 4-folds. The master space is the freely generated space of chiral fields subject to the J- and E-terms and the non-abelian part of the gauge symmetry. We investigate several properties of the master space for abelian brane brick models with U(1) gauge groups. For example, we calculate the Hilbert series, which allows us by using the plethystic programme to identify the generators and defining relations of the master space. By studying several explicit examples, we also show that the Hilbert series of the master space can be expressed in terms of characters of irreducible representations of the full global symmetry of the master space.