Critical Dynamics of Holographic Superfluids

TL;DR

This work analyzes the near-critical dynamics of holographic superfluids at finite $T$ and $\mu$ by applying the Crnkovic–Witten symplectic current to bulk fluctuations, including backreaction, to derive a long-wavelength effective theory for gapless and amplitude modes at next-to-leading order. It provides complete constitutive relations for the stress tensor and current and a complex amplitude evolution equation with transport coefficients expressed entirely in terms of background data, then validates the framework against numerical quasinormal modes near $T_c$. The approach yields a covariant, near-critical generalization of Model F with a novel complex coefficient $Z_\pi$, and confirms consistency with entropy-positivity and Onsager reciprocity. The combination of analytic derivation and numerical checks clarifies universal features of near-critical holographic dynamics and offers a versatile framework for studying other strongly coupled systems with broken symmetries.

Abstract

We study the nearly critical behaviour of holographic superfluids at finite temperature and chemical potential. Using analytic techniques in the bulk, we derive an effective theory for the long wavelength dynamics of gapless and pseudo-gapped modes, at first subleading order in a derivative expansion and we match the classical limit of our field theory construction in a companion paper. Specifically, we obtain the constitutive relations for the stress tensor and electric current, as well as a time evolution equation for the order parameter at next-to-leading order. In addition, we get explicit formulas for all the transport coefficients in terms of background quantities. We carry out numerical cross-checks with the predictions of our effective theory close to the critical point.

Figures (3)

• Figure 1: Plots of $\frac{\partial}{\partial q}\mathrm{Re}[\omega_{FS,+}]$ and $\frac{1}{2}\frac{\partial^2}{\partial q^2}\mathrm{Im}[\omega_{FS,+}]$ for the first sound mode as a function of $\frac{q}{\mu}$ for $\frac{T}{T_c}\approx0.9999922$. The dashed lines correspond to the numerical results and the solid green lines to the analytic predictions.
• Figure 2: Plots of $\frac{\partial}{\partial q}\mathrm{Re}[\omega_{SS,+}]$, $\frac{1}{2}\frac{\partial^2}{\partial q^2}\mathrm{Re}[\omega_{SS,+}]$ and $\frac{1}{2}\frac{\partial^2}{\partial q^2}\mathrm{Im}[\omega_{SS,+}]$ for the second sound mode as a function of $\frac{q}{\mu}$ for $\frac{T}{T_c}\approx0.9999922$. The dashed lines correspond to the numerical results and the solid green lines to the analytic predictions.
• Figure 3: Plots of $\frac{1}{2}\frac{\partial^2}{\partial q^2} \mathrm{Im}[\omega_H]$ and $\frac{1}{2}\frac{\partial^2}{\partial q^2} \mathrm{Im}[\omega_D]$, for the Higgs and shear diffusive mode respectively, as a function of $\frac{q}{\mu}$, for $\frac{T}{T_c}\approx0.9999922$. The dashed lines correspond to the numerical results and the solid green lines to the analytic predictions.