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

Abstract The Gubser–Rocha model is a holographic model that shows the linear dependence of the entropy density on the temperature. The model can be extended to possess S-duality by introducing an axio-dilaton field. With an appropriate choice of the boundary action, both models exhibit a continuous phase transition in the neutral limit. In this paper, we investigate several aspects of this phase transition. First, we show that the critical exponents of the phase transition match those of the mean-field percolation theory. Next, we analyze the dynamical stability, and the emergence of the Nambu–Goldstone modes by analyzing the quasinormal modes of the perturbation fields. The dynamical stability is consistent 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.