GLSM's for partial flag manifolds

TL;DR

The paper develops nonabelian GLSMs to realize partial flag manifolds, their tangent bundles, and Calabi–Yau complete intersections, while exposing nonbirational Kahler phases and linking them to Kuznetsov's homological projective duality. It provides explicit GLSM constructions for Grassmannians and flag manifolds, including mixed and weighted variants, and analyzes quantum cohomology via one-loop arguments and moduli spaces. A central contribution is the identification of LSM moduli spaces with Quot and hyperquot schemes, clarifying how maps into these spaces behave physically and algebraically. The work also extends to abelian cases and Pfaffian duals, offering a broad HPD framework for understanding phase structure and derived categories in GLSMs, with potential implications for noncommutative resolutions in LG phases.

Abstract

In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to realizations of tangent bundles and other aspects pertinent to (0,2) models. Second, we review constructions of Calabi-Yau complete intersections within such flag manifolds, and properties of the gauged linear sigma models. We discuss a number of examples of nonabelian GLSM's in which the Kahler phases are not birational, and in which at least one phase is realized in some fashion other than as a complete intersection, extending previous work of Hori-Tong. We also review an example of an abelian GLSM exhibiting the same phenomenon. We tentatively identify the mathematical relationship between such non-birational phases, as examples of Kuznetsov's homological projective duality. Finally, we discuss linear sigma model moduli spaces in these gauged linear sigma models. We argue that the moduli spaces being realized physically by these GLSM's are precisely Quot and hyperquot schemes, as one would expect mathematically.