Schubert defects in Lagrangian Grassmannians

TL;DR

This paper constructs GLSM defects for Schubert cycles in Lagrangian Grassmannians, integrating geometric and quantum invariants, and verifies their consistency with mathematical descriptions and known invariants.

Contribution

It introduces a novel construction of GLSM defects for Lagrangian Grassmannians, extending previous work on ordinary Grassmannians, and connects physical models with mathematical invariants.

Findings

Constructed GLSM defects for Lagrangian Grassmannians.

Verified defect support matches mathematical descriptions.

Computed defect indices align with known quantum invariants.

Abstract

In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. In the case of Lagrangian Grassmannians, there are superpotential terms in both the bulk GLSM as well as on the defect itself, enforcing isotropy constraints. We check our construction by comparing the locus on which the GLSM defect is supported to mathematical descriptions, checking dimensions, and perhaps most importantly, comparing defect indices to known and expected polynomial invariants of the Schubert cycles in quantum cohomology and quantum K theory.