Zoology of Solid & Fluid Holography : Goldstone Modes and Phase Relaxation
Matteo Baggioli, Sebastian Grieninger
备注：
v3: new section about the comparison with Hydro+, new section proving the universal relation for the Goldstone phase relaxation; version accepted in JHEP
We provide a comprehensive classification of isotropic solid and fluid holographic models with broken translational invariance. We describe in detail the collective modes in both the transverse and longitudinal sectors. First, we discuss holographic fluid models, i.e. systems invariant under internal volume preserving diffeomorphisms. We consider the explicit (EXB) and the spontaneous (SSB) breaking of translations and we emphasize the differences with respect to their solid counterpart. Then, we present a study of the longitudinal collective modes in simple holographic solid and fluid models exhibiting the interplay between SSB and EXB. We confirm the presence of light pseudo-phonons obeying the Gell-Mann-Oakes-Renner relation and the validity of the relation proposed in the literature between the novel phase relaxation scale, the mass of the pseudo-Golstone modes and the Goldstone diffusion. Moreover, we find very good agreement between the dispersion relation of our longitudinal sound mode and the formulae derived from the Hydro$+$ framework. Finally, our results suggest that the crystal diffusion mode does not acquire a simple damping term because of the novel relaxation scale proportional to the EXB. The dynamics is more complex and it involves the interplay of three modes: the crystal diffusion and two more arising from the splitting of the original sound mode. In this sense, the novel relaxation scale, which comes from the explicit breaking of the global internal shift symmetry of the Stückelberg fields, is different from the one induced by elastic defects, and depending solely on the SSB scale.
本文从全息的角度综述了AdS空间中高自旋规范对称性破缺的最新研究进展。根据AdS/CFT对应，N=4的SYM理论在耦合常数为零时，应该是AdS中自旋规范对称性增强更高的理论的对偶。当SYM耦合不为零时，除了少数HS电流之外，所有HS电流都被异常破坏，并且相应地，体中的局部较高自旋对称性自发地被破坏。与以前的结果和全息的期望，我们发现，除了一个值得注意的例外（自旋1吃自旋0），负责HS对称性破缺的戈德斯通模式在AdS有非零质量，即使在极限中的规范对称性恢复。我们表明，自发破缺a' la Stueckelberg意味着相关的自旋s'= s-1戈德斯通场的质量正是对应预测的。
