Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical nature of Skyrme-Faddeev models in $2+1$ dimensions and
  normalizable fermions   The Skyrme-Faddeev model has planar soliton solutions with target space
$\mathbb{C}P^N$. An Abelian Chern-Simons term (the Hopf term) in the Lagrangian
of the model plays a crucial role for the statistical properties of the
solutions. Because $\Pi_3(\mathbb{C}P^1)=\mathbb{Z}$, the term becomes an
integer for $N=1$. On the other hand, for $N>1$, it becomes perturbative
because $\Pi_3(\mathbb{C}P^N)$ is trivial. The prefactor $\Theta$ of the Hopf
term is not quantized, and its value depends on the physical system. We study
the spectral flow of the normalizable fermions coupled with the baby-Skyrme
model ($\mathbb{C}P^N$ Skyrme-Faddeev model). We discuss whether the
statistical nature of solitons can be explained using their constituents, i.e.,
the quarks.

18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat