# Two-dimensional gauge dynamics and the topology of singular determinantal varieties

## TL;DR

This paper explores the relationship between Witten indices in specific gauged linear sigma models and the Euler characteristics of associated singular determinantal varieties, providing insights into their topological and physical properties.

## Contribution

It establishes a connection between Witten indices and Euler characteristics of singular determinantal varieties in two classes of gauged linear sigma models, extending understanding of their topological invariants.

## Key findings

- Witten indices relate to Euler characteristics of determinantal varieties.
- Analysis of U(2) and U(1) gauged linear sigma models.
- Discussion on reconciliation with Born-Oppenheimer arguments.

## Abstract

We record an observation about the Witten indices in two families of gauged linear sigma models: the U(2) model for linear sections of Grassmannians, and the U(1) model for quadric complete intersections. We describe how the Witten indices are related to the Euler characteristics of the singular skew-symmetric or symmetric determinantal varieties featuring in the analysis of their opposite phases, and we discuss the extent to which these relationships can be reconciled with standard Born-Oppenheimer arguments.