Notes on nonabelian (0,2) theories and dualities

Abstract

In this paper we explore basic aspects of nonabelian (0,2) GLSM's in two dimensions for unitary gauge groups, an arena that until recently has largely been unexplored. We begin by discussing general aspects of (0,2) theories, including checks of dynamical supersymmetry breaking, spectators and weak coupling limits, and also build some toy models of (0,2) theories for bundles on Grassmannians, which gives us an opportunity to relate physical anomalies and trace conditions to mathematical properties. We apply these ideas to study (0,2) theories on Pfaffians, applying recent perturbative constructions of Pfaffians of Jockers et al. We discuss how existing dualities in (2,2) nonabelian gauge theories have a simple mathematical understanding, and make predictions for additional dualities in (2,2) and (0,2) gauge theories. Finally, we outline how duality works in open strings in unitary gauge theories, and also describe why, in general terms, we expect analogous dualities in (0,2) theories to be comparatively rare.

93 pages, LaTeX; v2: typos fixed

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Cited by in corpus (27)

• Decomposition in diverse dimensions
• Supersymmetric localization in two dimensions
• Localization of twisted $\mathcal{N}=(0,2)$ gauged linear sigma models in two dimensions
• Integrability from 2d N=(2,2) Dualities
• A 2d (0,2) appetizer
• B-branes and supersymmetric quivers in 2d
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
• Quantum sheaf cohomology on Grassmannians
• A-twisted correlators and Hori dualities
• 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
• Geometric Constructions of Two Dimensional (0,2) SUSY Theories
• Two-dimensional gauge dynamics and the topology of singular determinantal varieties
• More nonabelian mirrors and some two-dimensional dualities
• A few recent developments in 2d (2,2) and (0,2) theories
• Equivariant A-twisted GLSM and Gromov--Witten invariants of CY 3-folds in Grassmannians
• Quantum Sheaf Cohomology and Duality of Flag Manifolds
• Remarks on 2d Unframed Quiver Gauge Theories
• 2D Seiberg-like dualities with an adjoint matter
• (0,2) versions of exotic (2,2) GLSMs
• Determinantal Calabi-Yau varieties in Grassmannians and the Givental $I$-functions
• Cluster-Enriched Yang-Baxter Equation from SUSY Gauge Theories
• 2d dualities from 4d
• On Grassmannian Heterotic Sigma Model
• More on Two-Dimensional $O(N)$ Models with $\mathcal{N}=(0,1)$ Supersymmetry
• Anomalies of Minimal N=(0, 1) and N=(0, 2) Sigma Models on Homogeneous Spaces
• Making supersymmetric connected N =(0,2) Sigma Models