Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polyakov SU(3) extended linear $\sigma$-model: Sixteen mesonic states in
  chiral phase-structure   The derivative of the grand potential in mean field approximation,
non-strange and strange condensates and deconfinement phase-transition in
thermal and dense hadronic medium are verified in extended SU(3) linear
sigma-model (eLSM). In determining the chiral phase-transition, the chiral
condensates sigma_x and sigma_y are analysed. The chiral mesonic
phase-structures in temperature- and density-dependence are taken as free
parameters to be fitted. These parameters are classified corresponding to
scalar meson nonets; (pseudo)-scalar and (axial)-vector. For deconfinement
phase-transition, effective Polyakov loop-potentials phi and phi^* are
utilized. We investigated the in-medium effects on the masses of sixteen
mesonic states states. The results are presented for two different forms for
the effective Polyakov loop-potential and compared with other models with and
without anomalous terms. The Polyakov loop potential in LSM has considerable
effects on the chiral phase-transition in meson masses so that the restoration
of the chiral symmetry becomes sharper and faster than LSM. We normalize all
mesonic states with respect to the lowest Matsubara frequency. It has been
found that the various mesonic states have different dissolving temperatures
and chemical potentials, i.e. they survive the typically-averaged QCD phase
boundary, defined by the QCD critical temperatures with varying chemical
potentials. The thermal behavior of all meson masses has been investigated in
the large-$N_c$ limit and found that the scalar meson masses are T-independent
at large $N_c$ and high $T$ (except pi and sigma). For the pseudoscalar meson
masses, the large N_c limit unifies the $T$-dependence of all states in a
universal bundle. The same is also observed for axial and axialvector meson
masses in the large-N_c limit.

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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: cs