General composite non-Abelian strings and flag manifold sigma models

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 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 N = (2, 2) supersymmetric. We finish by performing some groundwork analysis of the resulting theory.

Flag manifold sigma models: spin chains and integrable theories

“…unless 𝑚 = 2), see section 13.3. In contrast, Kähler metrics are encountered in other applications of flag manifold sigma models, for example in the description of worldsheet theories of non-Abelian vortices in certain fourdimensional supersymmetric theories [141,140] -in this case Kähler metrics are required by supersymmetry.…”