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

TL;DR

The work analyzes the neutral (S-type) Gubser-Rocha holographic model with momentum dissipation to understand a continuous phase transition driven by a bulk global $U(1)$ symmetry. Using a triple-trace boundary deformation, the authors obtain static critical exponents $\alpha=-1$, $\\beta=1$, $\\gamma=1$, $\\delta=2$, and, via hyperscaling, $\\nu=3/2$, $\\eta=4/3$, consistent with mean-field percolation rather than standard holographic superfluid values. Dynamical stability is probed through gauge-invariant perturbations and quasinormal modes, showing agreement between thermodynamic and dynamical stability and revealing a dissipative Nambu–Goldstone mode in the broken phase, with an additional gapped NG mode and a characteristic mode-recombination temperature near $T_c$. Overall, the results illuminate a distinct universality class for holographic phase transitions controlled by multi-trace deformations, supported by analytic backgrounds, gauge-invariant perturbation analysis, and QNM spectroscopy.

Abstract

The (S-type) Gubser-Rocha model is a holographic model that shows the linear dependence of the entropy density on the temperature. 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.

Figures (7)

• Figure 1: Left: Vacuum expectation value of the dual operator to the axio-dilaton as a function of temperature. Right: Heat capacity as a function of temperature.
• Figure 2: Quasinormal frequencies of the dilaton (Higgs) modes as a function of temperature. Left: the result with $b = m - r_{0}$. The gray region indicates $b<0$ where $J_{\phi}=J_{\chi}=0$ does not hold. Right: the result with $b = 0$.
• Figure 3: Left: Susceptibility as a function of temperature. The points denote numerical results, and the curves denote fitting with Eq. (\ref{['eq:susceptibility_fit']}). Right: The same data shown on a double-logarithmic scale with $|T/T_{\rm c} - 1|$ as the x-axis.
• Figure 4: Dispersion relations of the axion (NG) modes for $\theta=0$. The points denote the numerical results, while the curves denote fitting results with Eq. (\ref{['eq:dispersion_relation']}). Top-left: restored phase at $T/T_{\rm c}= 2.0$. Top-right: restored phase at $T/T_{\rm c} = 1.2$. Bottom: broken phase at $T/T_{\rm c} = 0.8$.
• Figure 5: Quasinormal frequency of the second NG mode as a function of the temperature. The vertical dotted line shows $T=0.77718 T_{\rm c}$ and $T=T_{\rm c}$.