Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BPS Sphalerons in the $F_2$ Non-Linear Sigma Model   We construct static and also time-dependent solutions in a non-linear sigma
model with target space being the flag manifold $F_2=SU(3)/U(1)^2$ on the four
dimensional Minkowski space-time by analytically solving the second order
Euler-Lagrange equation. We show the static solutions saturate an energy lower
bound and can be derived from coupled first order equations though they are
saddle point solutions. We also discuss basic properties of the time-dependent
solutions.

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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int