(0,2) Trialities

Abstract

Motivated by the connection between 4-manifolds and 2d N=(0,2) theories, we study the dynamics of a fairly large class of 2d N=(0,2) gauge theories. We see that physics of such theories is very rich, much as the physics of 4d N=1 theories. We discover a new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the new 2d duality is an operation of order three: it is IR equivalence of three different theories and, as such, is actually a triality. We also consider quiver theories and study their triality webs. Given a quiver graph, we find that supersymmetry is dynamically broken unless the ranks of the gauge groups and flavor groups satisfy stringent inequalities. In fact, for most of the graphs these inequalities have no solutions. This supports the folklore theorem that generic 2d N=(0,2) theories break supersymmetry dynamically.

31 pages, 12 figures

References in corpus (4)

• Elliptic genera of 2d N=2 gauge theories
• Surface Defects and Resolvents
• New Integrable Models from the Gauge/YBE Correspondence
• The Quantum Dynamics of Heterotic Vortex Strings

Cited by in corpus (73)

• Dual Boundary Conditions in 3d SCFT's
• Two-dimensional SCFTs from D3-branes
• 2d (0,2) Quiver Gauge Theories and D-Branes
• Brane Brick Models in the Mirror
• $(0,4)$ dualities
• Brane Brick Models and 2d (0,2) Triality
• On the reduction of 4d N=1 theories on S^2
• Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers
• Long Multiplet Bootstrap
• (0,2) SCFTs from the Leigh-Strassler Fixed Point
• Quiver Mutations, Seiberg Duality and Machine Learning
• A slow review of the AGT correspondence
• Notes on nonabelian (0,2) theories and dualities
• (0,2) Dynamics From Four Dimensions
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Decomposition in diverse dimensions
• Orbifold Reduction and 2d (0,2) Gauge Theories
• Quadrality for Supersymmetric Matrix Models
• Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models
• Supersymmetric localization in two dimensions
• New 2d $\mathcal{N}=(0,2)$ dualities from four dimensions
• Quiver gauge theories and integrable lattice models
• Higher Cluster Categories and QFT Dualities
• Calabi-Yau Volumes and Reflexive Polytopes
• A 2d (0,2) appetizer
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• B-branes and supersymmetric quivers in 2d
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• $3d$ Printing of $2d$ $\mathcal{N}=(0,2)$ Gauge Theories
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
• Green-Schwarz Automorphisms and 6D SCFTs
• Supersymmetric indices on $I\times T^2$, elliptic genera and dualities with boundaries
• Chiral operators in two-dimensional (0,2) theories and a test of triality
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• Fano 3-Folds, Reflexive Polytopes and Brane Brick Models
• Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
• Graded Quivers, Generalized Dimer Models and Toric Geometry
• 2d $\mathcal{N}=(0,1)$ Gauge Theories and Spin(7) Orientifolds
• Ising Machines for Diophantine Problems in Physics
• The Origin of Calabi-Yau Crystals in BPS States Counting
• Geometric Constructions of Two Dimensional (0,2) SUSY Theories
• Brane Brick Models for the Sasaki-Einstein 7-Manifolds Y^{p,k}(CP^1 x CP^1) and Y^{p,k}(CP^2)
• Lectures on 4d N=1 dynamics and related topics
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• On Isometry Anomalies in Minimal N=(0,1) and N=(0,2) Sigma Models
• (0,2) Dualities and the 4-Simplex
• Calabi-Yau Products: Graded Quivers for General Toric Calabi-Yaus
• Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities
• BFT${}_2$: a General Class of $2d$ $\mathcal{N}=(0,2)$ Theories, 3-Manifolds and Toric Geometry
• Charging solid partitions
• A Landscape of Field Theories
• Spin(7) Orientifolds and 2d $\mathcal{N}=(0,1)$ Triality
• Supersymmetric gauged matrix models from dimensional reduction on a sphere
• Trialities of minimally supersymmetric 2d gauge theories
• On the Classification of Duality Webs for Graded Quivers
• All supersymmetric solutions of 3D U(1)${}^3$ gauged supergravity
• From N=2 in four dimensions to (0,2) in two dimensions
• Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
• Holomorphy, triality and non-perturbative beta function in 2d supersymmetric QCD
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• 2d dualities from 4d
• Quiver Gauge Theories: Beyond Reflexivity
• An Overview of Crystals and Double Quiver Yangians
• Supersymmetric zeta functions and determinants
• A survey of recent developments in GLSMs
• Tetrahedron duality
• More on Two-Dimensional $O(N)$ Models with $\mathcal{N}=(0,1)$ Supersymmetry
• Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus, from the Fivebrane on T2 x T4, via their Partition Functions
• Making supersymmetric connected N =(0,2) Sigma Models
• On Grassmannian Heterotic Sigma Model
• Global aspects of (0,2) moduli space: toric varieties and tangent bundles
• Aspects of 4d supersymmetric dynamics and geometry
• Hilbert Series of Bipartite Field Theories