Spontaneous chiral symmetry breaking in holographic soft wall models

We investigate non-linear extensions of the holographic soft wall model proposed by Karch, Katz, Son and Stephanov [1] including non-minimal couplings in the five-dimensional action. The non-minimal couplings bring a new parameter $a_0$ which controls the transition between spontaneous and explicit symmetry breaking near the limit of massless quarks (the chiral limit). In the physical region (positive quark mass), we show that above a critical value of the parameter $a_0$ the chiral condensate $\langle \bar{q} q \rangle$ is finite in the chiral limit, signifying spontaneous chiral symmetry breaking. This result is supported by the lightest states arising in the spectrum of the pseudoscalar mesons, which become massless in the chiral limit and are therefore intrepreted as Nambu-Goldstone bosons. Moreover, the decay constants of the pseudoscalar mesons also support this conclusion, as well as the Gell-Mann-Oakes-Renner (GOR) relation satisfied by the lightest states. We also calculate the spectrum of scalar, vector, and axial-vector mesons with their corresponding decay constants. We describe the evolution of masses and decay constants with the increasing of the quark mass and for the physical mass we compare our results against available experimental data. Finally, we do not find instabilities in our model for the physical region (positive quark mass).