The Master Space of N=1 Gauge Theories

Abstract

The full moduli space M of a class of N=1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X, M is a combination of the mesonic and baryonic branches, the former being the symmetric product of X. In consonance with the mathematical literature, the single brane moduli space is called the master space F. Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode ``hidden'' global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for arbitrary number of branes.

arXiv comment84 pages, 14 figures, comments and refs added

References in corpus (28)

• Gauge Theories from Toric Geometry and Brane Tilings
• Orbifold Resolution by D-Branes
• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• Counting Gauge Invariants: the Plethystic Program
• Dimer models and toric diagrams
• Toric Duality as Seiberg Duality and Brane Diamonds
• Phase Structure of D-brane Gauge Theories and Toric Duality
• Brane Tilings
• Symmetries of Toric Duality
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
• On the realization of chiral four-dimensional gauge theories using branes
• Counting Chiral Operators in Quiver Gauge Theories
• Counting BPS operators in N=4 SYM
• STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Exploring the Vacuum Geometry of N=1 Gauge Theories
• Reverse geometric engineering of singularities
• A Monograph on the Classification of the Discrete Subgroups of SU(4)
• From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
• Deformations of conformal theories and non-toric quiver gauge theories
• Hidden Exceptional Global Symmetries in 4d CFTs
• Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery
• Dimer Models from Mirror Symmetry and Quivering Amoebae
• BPS Partition Functions for Quiver Gauge Theories: Counting Fermionic Operators
• Stability of Quiver Representations and Topology Change
• Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians
• Birational Equivalences of Vortex Moduli

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