Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $k$-Strings with exact Casimir law and Abelian-like profiles   We explore vortex solutions for a class of dual $SU(N)$ Yang-Mills models
with $N^2-1$ Higgs fields in the adjoint representation. Initially, we show
that there is a collective behavior that can be expressed in terms of a small
$N$-independent number of field profiles. Then, we find a region in parameter
space where the nontrivial profiles coincide with those of the Nielsen-Olesen
vortex, and the energy scales exactly with the quadratic Casimir. Out of this
region, we solve the ansatz equations numerically and find very small
deviations from the Casimir law. The coexistence of Abelian-like string
profiles and non-Abelian scaling features is welcome, as these properties have
been approximately observed in pure YM lattice simulations.

23
The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
2
The categories of this paper are: math