Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of Yang-Mills theory in four-dimensional de Sitter space   This doctoral work deals with the analysis of some Yang-Mills solutions on
4-dimensional de Sitter space d$S_4$. The conformal equivalence of this space
with a finite Lorentzian cylinder over the 3-sphere and also with parts of
Minkowski space has recently led to the discovery of a family of rational
knotted electromagnetic field configurations. These "basis-knot" solutions of
the Maxwell equations, aka $U(1)$ Yang-Mills theory, are labelled with the
hyperspherical harmonics of the 3-sphere and have nice properties such as
finite-energy, finite-action and presence of a conserved topological quantity
called helicity. We study their symmetry properties, compute their conserved
Noether charges for the conformal group and study behaviour of charged
particles in their presence.
  Moreover, in the non-Abelian case of the gauge group $SU(2)$ there exist
time-dependent solutions of Yang-Mills equation on d$S_4$ in terms of Jacobi
elliptic functions that are of cosmological significance. These could play a
role in early-time cosmology where an $SO(4)$-symmetric Higgs vacuum is
stabilized due to rapid fluctuations of these gauge fields. We analyze the
linear stability of such $SU(2)$ "cosmic gauge fields" against arbitrary
perturbations of the Yang-Mills equation, while keeping the FLRW metric frozen.
The stablity analysis of the time-dependent normal modes that arise from the
diagonalization of the Yang-Mills fluctuation operator is carried out using
Floquet theory.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin