Reverse geometric engineering of singularities

Abstract

One can geometrically engineer supersymmetric field theories theories by placing D-branes at or near singularities. The opposite process is described, where one can reconstruct the singularities from quiver theories. The description is in terms of a noncommutative quiver algebra which is constructed from the quiver diagram and the superpotential. The center of this noncommutative algebra is a commutative algebra, which is the ring of holomorphic functions on a variety V. If certain algebraic conditions are met, then the reverse geometric engineering produces V as the geometry that D-branes probe. It is also argued that the identification of V is invariant under Seiberg dualities.

17 pages, Latex. v2: updates references

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Cited by in corpus (42)

• Symmetries of Toric Duality
• The Master Space of N=1 Gauge Theories
• Supersymmetry Breaking from a Calabi-Yau Singularity
• Seiberg Duality for Quiver Gauge Theories
• SQCD: A Geometric Apercu
• Unhiggsing the del Pezzo
• Quantum moduli spaces from matrix models
• Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories
• Mastering the Master Space
• Giant gravitons: a collective coordinate approach
• Counting Gauge Invariant Operators in SQCD with Classical Gauge Groups
• A Point's Point of View of Stringy Geometry
• M2-Branes and Quiver Chern-Simons: A Taxonomic Study
• Emergent geometry from q-deformations of N=4 super Yang-Mills
• Aspects of emergent geometry in the AdS/CFT context
• Nonsupersymmetric Brane/Antibrane Configurations in Type IIA and M Theory
• Multi-Trace Superpotentials vs. Matrix Models
• New results on superconformal quivers
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• On the noncommutative geometry of square superpotential algebras
• Representation theory of three-dimensional Sklyanin algebras
• Strings on conifolds from strong coupling dynamics, part I
• BPS State Counting in Local Obstructed Curves from Quiver Theory and Seiberg Duality
• On Duality Walls in String Theory
• Solving Flavor Puzzles with Quiver Gauge Theories
• Master Space and Hilbert Series for N=1 Field Theories
• Monopole operators, moduli spaces and dualities
• Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra
• A Quiver of Many Runaways
• M5 spikes and operators in the HVZ membrane theory
• Noncommutative resolutions of ADE fibered Calabi-Yau threefolds
• The Geometry of Noncommutative Singularity Resolutions
• Geometric aspects of dibaryon operators
• Aspects of ABJM orbifolds
• Toric Varieties with NC Toric Actions: NC Type IIA Geometry
• Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices
• On Fields over Fields
• Solving matrix models using holomorphy
• The geometry of representations of 3-dimensional Sklyanin algebras
• Aspects of Supersymmetric Gauge Theory and String Theory
• Aspects of ABJM orbifolds with discrete torsion
• Isolated singularities, smooth orders and Auslander regularity