Notes on nonabelian (0,2) theories and dualities

TL;DR

This work develops a detailed framework for nonabelian (0,2) gauged linear sigma models in two dimensions with unitary gauge groups, focusing on weak-coupling limits, Grassmannian and Pfaffian geometries, and the role of anomalies and bundle data. By leveraging geometric presentations of target spaces and bundles, the authors translate physical dualities into mathematical equivalences between different presentations of the same space (e.g., G(k,n) ≃ G(n-k,n)) and their associated bundles, extending to Pfaffian constructions and open-string Chan-Paton factors. They introduce and test dualities such as gauge-bundle dualization E ⇄ E*, abelian/nonabelian dualities to projective spaces, and Pfaffian-related PAX/PAXY dualities, using elliptic genera and central-charge checks as consistency probes. The work also discusses extensions to GGP triality, the role of worldsheet instantons, and obstructions to duality in more general (0,2) theories, highlighting that while many dualities arise from geometric equivalences in the UV, obstructions can limit their physical realization in the IR. Overall, the paper provides a cohesive, mathematically-informed view of 2D (0,2) dualities, with concrete tests in Grassmannians, complete intersections, and Pfaffians, and points to open questions in Landau-Ginzburg points, affine/gerbe variants, and D-brane realizations of these 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.