Dynamical Stability and Critical Exponents of the Neutral (S-type) Gubser-Rocha Model with Momentum Dissipation

The (S-type) Gubser-Rocha model is a holographic model, which can be derived from the maximal gauged supergravity in four dimensions. With an appropriate choice of the boundary action, this model exhibits a continuous phase transition in the neutral limit. In this paper, we investigate several aspects of this phase transition. Firstly, we show that the critical exponents of the phase transition match those in the mean-field percolation theory. Subsequently, we also investigate the dynamical stability, and the emergence of the Nambu-Goldstone modes by analyzing the quasinormal modes of the perturbation fields. The dynamical stability agrees with the thermodynamic stability. In addition, we find that there is an emergent Nambu-Goldstone mode in the broken phase of the S-type model.