Nucleons and vector mesons in a confining holographic QCD model

We present a simple holographic QCD model that provides a unified description of vector mesons and nucleons in a confining background based on Einstein-dilaton gravity. For the confining background we consider analytical solutions of the Einstein-dilaton equations where the dilaton is a quadratic function of the radial coordinate far from the boundary. We build actions for the 5d gauge field and the 5d Dirac field dual to the 4d flavor current and the 4d nucleon interpolator respectively. In order to obtain asymptotically linear Regge trajectories we impose for each sector the condition that the effective Schr\"odinger equation has a potential that grows quadratically in the radial coordinate far from the boundary. For the vector mesons we show that this condition is automatically satisfied by a 5d Yang-Mills action minimally coupled to the metric and the dilaton. For the nucleons we find that the mass term of the 5d Dirac action needs to be generalised to include couplings to the metric and the dilaton. Using Sturm-Liouville theory we obtain a spectral decomposition for the hadronic correlators consistent with large $N_c$ QCD. Our setup contains only three parameters: the mass scale associated with confinement, the 5d gauge coupling and the 5d Dirac coupling. The last two are completely fixed by matching the correlators at high energies to perturbative QCD. We calculate masses and decay constants and compare our results against available experimental data. Our model can be thought of as a consistent embedding of soft wall models in Einstein-dilaton gravity.