  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.
