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Advances in High Energy Physics
Volume 2010 (2010), Article ID 427891, 30 pages
Review Article

The Master Space of Supersymmetric Gauge Theories

1Theoretical Physics Group, Blackett Laboratory, Imperial College, London SW7 2AZ, UK
2Dipartimento di Fisica, Università di Milano-Bicocca, 20126 Milano, Italy
3INFN, Sezione di Milano-Bicocca, 20126 Milano, Italy

Received 10 May 2010; Accepted 14 June 2010

Academic Editor: Carlos Nunez

Copyright © 2010 Amihay Hanany and Alberto Zaffaroni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 or 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.