General Composite Non-Abelian Strings and Flag Manifold Sigma Models

TL;DR

This paper investigates composite non-Abelian strings in non-Abelian theories, revealing their internal degrees of freedom form a Flag manifold and constructing effective supersymmetric sigma models to describe their low-energy dynamics.

Contribution

It introduces the concept of composite non-Abelian strings with internal Flag manifold moduli and develops supersymmetric effective actions for their fluctuations.

Findings

Strings have internal degrees of freedom on Flag manifolds.

Constructed supersymmetric gauged linear and non-linear sigma models.

Demonstrated BPS nature and provided groundwork analysis of the effective theory.

Abstract

We fully investigate the symmetry breaking patterns occurring upon creation of composite non-Abelian strings: vortex strings in non-Abelian theories where different sets of colours have different amounts of flux. After spontaneous symmetry breaking, there remains some internal colour degrees of freedom attached to these objects, which we argue must exist in a Flag manifold, a more general kind of projective space than both $\mathbb{CP}(N)$ and the Grassmannian manifold. These strings are expected to be BPS, since its constituents are. We demonstrate that this is true and construct a low-energy effective action for the fluctuations of the internal Flag moduli, which we then re-write it in two different ways for the dynamics of these degrees of freedom: a gauged linear sigma model with auxiliary fields and a non-linear sigma model with an explicit target space metric for the Flag Manifolds, both of which $\mathcal{N}=(2,2)$ supersymmetric. We finish by performing some groundwork analysis of the resulting theory.