Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
arXiv:2502.08741 · doi:10.1007/JHEP06(2025)032
Abstract
We show that a family of birational transformations that relate toric Fano 3-folds defined by reflexive lattice polytopes can be identified with mass deformations of corresponding 2d (0,2) supersymmetric quiver gauge theories. These theories are realized by a Type IIA brane configuration known as brane brick models. We further show that the same family of birational transformations extends to more general toric Calabi-Yau 4-folds, including those defined by non-reflexive toric diagrams. Under these birational transformations, the mesonic moduli spaces of the associated abelian 2d (0,2) supersymmetric gauge theories and brane brick models share the same number of generators and the same Hilbert series when refined only under the U(1)R symmetry. Since these transformations categorize toric Calabi-Yau 4-folds and their corresponding 2d (0,2) supersymmetric gauge theories into non-trivial equivalence classes, we anticipate that our findings will pave the way for a `Minimal Model Program' for quiver gauge theories corresponding to toric Calabi-Yau manifolds.
arXiv comment85 pages, 24 figures, 18 tables; v2: published version
References in corpus (39)
- Gauge Theories from Toric Geometry and Brane Tilings
- Orbifold Resolution by D-Branes
- D-Brane Gauge Theories from Toric Singularities and Toric Duality
- Brane Dimers and Quiver Gauge Theories
- Counting Gauge Invariants: the Plethystic Program
- Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
- Webs of five-branes and N=2 superconformal field theories
- A Geometric Unification of Dualities
- The Master Space of N=1 Gauge Theories
- Counting Chiral Operators in Quiver Gauge Theories
- Gorenstein toric Fano varieties
- On the Classification of Reflexive Polyhedra
- Minkowski Polynomials and Mutations
- Brane Tilings and Reflexive Polygons
- Quantum Periods for 3-Dimensional Fano Manifolds
- 2d (0,2) Quiver Gauge Theories and D-Branes
- Brane Brick Models in the Mirror
- Highest Weight Generating Functions for Hilbert Series
- Exploring the Vacuum Geometry of N=1 Gauge Theories
- Brane Brick Models and 2d (0,2) Triality
- Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers
- Mastering the Master Space
- (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
- Counting Orbifolds
- Orbifold Reduction and 2d (0,2) Gauge Theories
- Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models
- Quadrality for Supersymmetric Matrix Models
- Maximal Periods of (Ehrhart) Quasi-Polynomials
- Symmetries of Abelian Orbifolds
- Calabi-Yau Volumes and Reflexive Polytopes
- Printing of Gauge Theories
- Mass-deformed Brane Tilings
- Twin Theories, Polytope Mutations and Quivers for GTPs
- Fano 3-Folds, Reflexive Polytopes and Brane Brick Models
- Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
- Mass Deformations of Brane Brick Models
- On the Master Space for Brane Brick Models
- Combinatorial and Algebraic Mutations of Toric Fano 3-folds and Mass Deformations of 2d (0,2) Quiver Gauge Theories
- Generative AI for Brane Configurations and Coamoeba