Logarithmic correction in the deformed AdS{sub 5} model to produce the heavy quark potential and QCD beta function

We study the holographic QCD model, which contains a quadratic term -{sigma}z{sup 2} and a logarithmic term -c{sub 0}log[(z{sub IR}-z)/z{sub IR}] with an explicit infrared cutoff z{sub IR} in the deformed AdS{sub 5} warp factor. We investigate the heavy-quark potential for three cases, i.e., with only a quadratic correction, with both quadratic and logarithmic corrections, and with only a logarithmic correction. We solve the dilaton field and dilation potential from the Einstein equation and investigate the corresponding beta function in the Guersoy-Kiritsis-Nitti framework. Our studies show that in the case with only a quadratic correction, a negative {sigma} or the Andreev-Zakharov model is favored to fit the heavy-quark potential and to produce the QCD beta function at 2-loop level; however, the dilaton potential is unbounded in the infrared regime. One interesting observation for the case of positive {sigma} is that the corresponding beta function exists in an infrared fixed point. In the case with only a logarithmic correction, the heavy-quark Cornell potential can be fitted very well, the corresponding beta function agrees with the QCD beta function at 2-loop level reasonably well, and the dilaton potential is bounded from below in the infrared. At the end, we propose a more compact model which has only a logarithmic correction in the deformed warp factor and has less free parameters.