Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quark confinement: dual superconductor picture based on a non-Abelian
  Stokes theorem and reformulations of Yang-Mills theory   The purpose of this paper is to review the recent progress in understanding
quark confinement. The emphasis of this review is placed on how to obtain a
manifestly gauge-independent picture for quark confinement supporting the dual
superconductivity in the Yang-Mills theory, which should be compared with the
Abelian projection proposed by 't Hooft. The basic tools are novel
reformulations of the Yang-Mills theory based on change of variables extending
the decomposition of the $SU(N)$ Yang-Mills field due to Cho, Duan-Ge and
Faddeev-Niemi, together with the combined use of extended versions of the
Diakonov-Petrov version of the non-Abelian Stokes theorem for the $SU(N)$
Wilson loop operator. Moreover, we give the lattice gauge theoretical versions
of the reformulation of the Yang-Mills theory which enables us to perform the
numerical simulations on the lattice. In fact, we present some numerical
evidences for supporting the dual superconductivity for quark confinement. The
numerical simulations include the derivation of the linear potential for static
interquark potential, i.e., non-vanishing string tension, in which the
"Abelian" dominance and magnetic monopole dominance are established,
confirmation of the dual Meissner effect by measuring the chromoelectric flux
tube between quark-antiquark pair, the induced magnetic-monopole current, and
the type of dual superconductivity, etc. In addition, we give a direct
connection between the topological configuration of the Yang-Mills field such
as instantons/merons and the magnetic monopole.

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs