The Master Space of Supersymmetric Gauge Theories

We give a short review on the study of the moduli space and the spectrum of chiral operators for gauge theories living on branes at singularities. We focus on theories with four real supercharges in 3+1 and 2+1 dimensions. The theories are holographically dual to A d S 5 × H 5 or A d S 4 × H 7 backgrounds, in Type‐IIB or ‐M theory, respectively. We demonstrate that most of the information on the moduli space and spectrum of the quiver gauge theories is encoded in the concept of the “Master Space”, which is roughly the full moduli space for one brane, consisting of mesonic and baryonic degrees of freedom. We summarize the relevant information in generating functions for chiral operators, which can be computed using plethystics techniques and the language of complex geometry.