Topological Soliton Multiplets in 4+1 Dimensional YMCS Theory

TL;DR

This paper extends the study of topological solitons in 4+1 dimensional SU(N) Yang-Mills-Chern-Simons theory, revealing their multiplet structures and properties for various embeddings and group sizes.

Contribution

It generalizes previous SU(3) results to SU(N), detailing the multiplet structures and characteristics of charged topological solitons in higher-dimensional YMCS theories.

Findings

Identifies N-plet structures of charged topological solitons for different embeddings.

Discovers neutral solitons with magnetic moments in the N=3 case.

Establishes multiplet classifications for N ≥ 4 in SU(N) YMCS theory.

Abstract

We generalize our results${}^1$ on charged topological solitons (CTS) in $4+1$ dimensional $SU(3)$ Yang-Mills-Chern-Simons (YMCS) theory to $SU(N)$. The $SU(N)$ multiplet structure of two classes of solitons associated with the maximal embeddings $SU(2)\times U(1)^{N-2}\subset SU(N)$ and $SO(3)\times U(1)^{N-3}\subset SU(N)$ and the vital role of the $SU(N)$ multiplet of topological currents is clarified. In the case of the first embedding one obtains a $^{N}C_{2}-$plet of CTS. In the second, for $N = 3$, one obtains neutral solitons which, though (classically) spinless, have magnetic moments. For $N \geq 4$, after modding out the above mentioned non-particulate feature, one obtains $^{N}C_{3}$ plets of CTS.