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AdS/QCD models describing a finite number of excited mesons with Regge spectrum

The typical AdS/QCD models deal with the large-N_c limit of QCD, as a consequence the meson spectrum consists of the infinite number of states that is far from the real situation. Basing on introduction of anharmonic corrections to the holographic potential, the corrections whose existence has been recently advocated, we construct a class of bottom-up holographic models describing arbitrary finite number of states in the sector of light mesons. Within the proposed approach, the spectrum of masses square has the following properties: It is linear, $m_n^2\sim n$, at not very large n, nonlinear at larger n, with the nonlinear corrections being subleading in 1/N_c, has a limiting mass, and the number of states is proportional to N_c. The considered holographic models reflect thereby the merging of resonances into continuum and the breaking of gluon string at sufficiently large quark-antiquark separation that causes the linear Regge trajectories to bend down. We show that these models provide a correct description for the spectrum of excited rho-mesons.