Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spontaneous electromagnetic superconductivity of vacuum in strong
  magnetic field: evidence from the Nambu--Jona-Lasinio model   Using an extended Nambu--Jona-Lasinio model as a low--energy effective model
of QCD, we show that the vacuum in a strong external magnetic field (stronger
than 10^{16} Tesla) experiences a spontaneous phase transition to an
electromagnetically superconducting state. The unexpected superconductivity of,
basically, empty space is induced by emergence of quark-antiquark vector
condensates with quantum numbers of electrically charged rho mesons. The
superconducting phase possesses an anisotropic inhomogeneous structure similar
to a periodic Abrikosov lattice in a type-II superconductor. The
superconducting vacuum is made of a new type of vortices which are topological
defects in the charged vector condensates. The superconductivity is realized
along the axis of the magnetic field only. We argue that this effect is absent
in pure QED.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics