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Spectra of glueballs and oddballs and the equation of state from holographic QCD

We study the spectra of two-gluon glueballs and three-gluon oddballs and corresponding equation of state in $5$-dimensional deformed holographic QCD models in the graviton-dilaton system, where the metric, the dilaton field and dilaton potential are self-consistently solved from each other through the Einstein field equations and the equation of motion of the dilaton field. We compare the models by inputting the dilaton field, inputting the deformed metric and inputting the dilaton potential, and find that with only 2 parameters, the $5$-dimensional holographic QCD model predictions on glueballs/oddballs spectra in general are in good agreement with lattice results except two oddballs $0^{+-}$ and $2^{+-}$. From the results of glueballs/oddballs spectra at zero temperature and the equation of state at finite temperature, we observe that the model with quadratic dilaton field can simultaneously describe glueballs/oddballs spectra as well as equation of state of pure gluon system. The model with quadratic $A_{E}(z)$ can describe glueballs/oddballs spectra, but its corresponding equation of state behaves more like $N_{f}=2+1$ quark matter. These are consistent with dimension analysis at UV boundary.