We study the presence of universal bounds on transport in homogeneous holographic models with broken translations. We verify numerically that, in holographic systems with momentum dissipation, the viscosity to entropy bound might be violated but the shear diffusion constant remains bounded by below. This confirms the idea that $η/s$ loses its privileged role in non-relativistic systems and that, in order to find more universal bounds, one should rather look at diffusion constants. We strengthen this idea by showing that, in presence of spontaneously broken translations, the Goldstone diffusion constant satisfies a universal lower bound in terms of the Planckian relaxation time and the butterfly velocity. Additionally, all the diffusive processes in the model satisfy an upper bound, imposed by causality, which is given in terms of the thermalization time -- the imaginary part of the first non-hydrodynamic mode in the spectrum -- and the speed of longitudinal sound. Finally, we discuss the existence of a bound on the speed of sound in holographic conformal solids and we show that the conformal value acts as a lower (and not upper) bound on the speed of longitudinal phonons. Nevertheless, we show that the stiffness $\partial p/\partial ε$ is still bounded by above by its conformal value. This suggests that the bounds conjectured in the past have to be considered on the stiffness of the system, related to its equation of state, and not on the propagation speed of sound.
In this paper we investigate the low energy shear modes in fluid systems with spontaneously broken translations by a specific holographic model. In absence of momentum relaxation, we find that there exist two decoupled gapless modes in the transverse channel, one of which is purely diffusive and the other corresponds to vortex like excitations. The diffusive mode is associated with the conservation of momentum and the vortex mode can be viewed as the Goldstone mode of the spontaneous symmetry breaking. Switching on an external source which breaks the translations explicitly but weakly, the wou…
We revisit HHH model in [Phys. Rev. Lett. {\bf 101}, 031601 (2008)] and extend the ansatz of matter fields to being of depending on a spatial dimension except the holographic direction. Despite homogeneous solutions of ground and excited states, especially for the excited states, there also exists solutions where the translational invariance is broken. It is worth mentioning that no periodic sources are assigned to the matter fields, so the translational symmetry is broken spontaneously. We investigate how the new solutions and the condensates of excited states develop with the change of tempe…
We show that the correct dual hydrodynamic description of homogeneous holographic models with spontaneously broken translations must include the so-called "strain pressure" -- a novel transport coefficient proposed recently. Taking this new ingredient into account, we investigate the near-equilibrium dynamics of a large class of holographic models and faithfully reproduce all the hydrodynamic modes present in the quasinormal mode spectrum. Moreover, while strain pressure is characteristic of equilibrium configurations which do not minimise the free energy, we argue and show that it also affect…
We present a large class of holographic models where the boundary ${\mathbb R}^{2,1}$ dimensional conformal field theory has a thermal phase with a spontaneously broken global symmetry. The dual black branes in a Poincare patch of asymptotically $AdS_4$ violate the no-hair theorem.
We study the concomitant breaking of spatial translations and dilatations in Ginzburg-Landau-like models, where the dynamics responsible for the symmetry breaking is described by an effective Mexican hat potential for spatial gradients. We show that there are fractonic modes with either subdimensional propagation or no propagation altogether, namely, immobility. Such class of effective field theories encompasses instances of helical superfluids and meta-fluids, where fractons can be connected to an emergent symmetry under higher moment charges, leading in turns to the trivialization of some el…
Universal relaxation in a holographic metallic density wave phase
结合规范/引力对偶和有效场论技术，我们揭示了钉扎密度波的普遍弛豫机制。当自发地破坏平移时，新的无间隙集体模式出现，即破坏平移的南武-戈德斯通玻色子。当平移也被弱破缺时（例如由无序或晶格效应），这些声子被质量为$m$的声子钉扎，并以我们明确计算的速率$Ω$阻尼。这种对$Ω$的贡献不同于拓扑缺陷的贡献。我们发现，$Ω\simeq G m^2Ξ$，其中$G$是剪切模量和$Ξ$是有关的纯自发状态的扩散。这一结果如下从体积和剪切模量的小，如将是在一个阶段的情况下与波动的平移顺序。在低温下，集体模式迅速松弛到热流中，因此后期的输运由热扩散率主导。在这个制度中，在我们的模型中的电阻率是线性的温度和交流电导率显示出显着的自由度重排，光谱权重从离轴，钉扎峰的德鲁德峰。这些结果可以揭示铜氧化物高$T_c$超导体的输运性质，其中量子临界行为和平移顺序发生在相图的大部分和运输显示定性相似的功能。
We explore higher-derivative terms in the low-energy effective action for the dilaton, the Goldstone boson of spontaneously broken scale invariance. Focusing on the simplest holographic realization of spontaneously broken scale invariance, the Randall-Sundrum (RS) scenario, we identify the nonlinear action for the RS dilaton by integrating out Kaluza-Klein graviton modes. The coefficient of a particular four-derivative dilaton self-interaction can be identified with the Weyl $a$-anomaly of the dual conformal field theory, which we use to verify anomaly matching arguments. We also find novel, $…
We investigate the infinite-distance properties of families of unstable flux vacua in string theory with broken supersymmetry. To this end, we employ a generalized notion of distance in the moduli space and we build a holographic description for the non-perturbative regime of the tunneling cascade in terms of a renormalization group flow. In one limit we recover an exponentially light tower of Kaluza-Klein states, while in the opposite limit we find a tower of higher-spin excitations of D1-branes, realizing the emergent string proposal. In particular, the holographic description includes a fre…
We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized by the effective time dependent Ginzburg-Landau equation, both above and below the critical temperature, which leads to a "gapless" algebraic pattern of metal-insulator phase transition. In this framework we elucidate the nature of the damped Goldstone mode (the phason), which has earlier been identified in the effective hydrodynamic theory of pinned charge…
