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.

84 pages, 14 figures, comments and refs added

References in corpus (9)

• Counting Gauge Invariants: the Plethystic Program
• Dimer models and toric diagrams
• Brane Tilings
• 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
• Exploring the Vacuum Geometry of N=1 Gauge Theories
• Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery
• BPS Partition Functions for Quiver Gauge Theories: Counting Fermionic Operators

Cited by in corpus (47)

• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Brane Tilings and M2 Branes
• SQCD: A Geometric Apercu
• Towards M2-brane Theories for Generic Toric Singularities
• Brane Tilings and Reflexive Polygons
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• The Hilbert Series of Adjoint SQCD
• Highest Weight Generating Functions for Hilbert Series
• Phases of M2-brane Theories
• N=2 solutions of massive type IIA and their Chern-Simons duals
• Brane Tilings and Specular Duality
• M2-Branes and Quiver Chern-Simons: A Taxonomic Study
• Symmetry-breaking vacua and baryon condensates in AdS/CFT
• Toric geometry and the dual of $c$-extremization
• Master Space, Hilbert Series and Seiberg Duality
• The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series
• The Scattering Variety
• E3-brane instantons and baryonic operators for D3-branes on toric singularities
• Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Twin Theories, Polytope Mutations and Quivers for GTPs
• Fano 3-Folds, Reflexive Polytopes and Brane Brick Models
• Master Space and Hilbert Series for N=1 Field Theories
• Hilbert Series and Moduli Spaces of k U(N) Vortices
• Sporadic and Exceptional
• Mass Deformations of Brane Brick Models
• Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds
• Gauge Theories, Tessellations & Riemann Surfaces
• Brane Tilings and Non-Commutative Geometry
• BFT${}_2$: a General Class of $2d$ $\mathcal{N}=(0,2)$ Theories, 3-Manifolds and Toric Geometry
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials
• On the Master Space for Brane Brick Models
• M2-branes Theories without 3+1 Dimensional Parents via Un-Higgsing
• Geometric aspects of dibaryon operators
• Futaki Invariants and Reflexive Polygons
• Mahler Measure for a Quiver Symphony
• Equivalence of A-Maximization and Volume Minimization
• Eulerian digraphs and toric Calabi-Yau varieties
• Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
• Index and localization for type B superconformal mechanics on singular spaces
• Parallel degree computation for solution space of binomial systems with an application to the master space of $\mathcal{N}=1$ gauge theories
• Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
• Holographic spectral functions for Sasaki-Einstein 5-manifolds
• Quiver-Invariant Dualities between Brane Tilings
• Reflexions on Mahler: Dessins, Modularity and Gauge Theories
• Hilbert Series of Bipartite Field Theories
• Baryonic symmetries in AdS_4/CFT_3: an overview