# Composite Non-Abelian Strings with Grassmannian Models on the World Sheet

## TL;DR

This paper generalizes the study of non-Abelian string-vortices by introducing composite strings supported by Grassmannian models, enabling new insights into vacuum counting in supersymmetric theories.

## Contribution

It extends the framework of non-Abelian strings to include Grassmannian models on the world sheet, offering a clearer method for counting vacua in supersymmetric models.

## Key findings

- Supported Grassmannian models on non-Abelian strings.
- Provided a simple method for counting vacua.
- Generalized existing models to composite strings.

## Abstract

Most of the non-Abelian string-vortices studied so far are characterized by two-dimensional \cpn models with various degrees of supersymmetry on their world sheet. We generalize this construction to "composite" non-Abelian strings supporting the Grassmann $\mathcal{G}(L,M)$ models (here $L+M=N$). The generalization is straightforward and provides, among other results, a simple and transparent way for counting the number of vacua in ${\mathcal N}=(2,2)$ Grassmannian model.