Solid Holography and Massive Gravity

Momentum dissipation is an important ingredient in condensed matter physics that requires a translation breaking sector. In the bottom-up gauge/gravity duality, this implies that the gravity dual is massive. We start here a systematic analysis of holographic massive gravity (HMG) theories, which admit field theory dual interpretations and which, therefore, might store interesting condensed matter applications. We show that there are many phases of HMG that are fully consistent effective field theories and which have been left overlooked in the literature. The most important distinction between the different HMG phases is that they can be clearly separated into solids and fluids. This can be done both at the level of the unbroken spacetime symmetries as well as concerning the elastic properties of the dual materials. We extract the modulus of rigidity of the solid HMG black brane solutions and show how it relates to the graviton mass term. We also consider the implications of the different HMGs on the electric response. We show that the types of response that can be consistently described within this framework is much wider than what is captured by the narrow class of models mostly considered so far.Comment: 43 pages, 4 figure

Black hole elasticity and gapped transverse phonons in holography

We study the elastic response of planar black hole (BH) solutions in a simple class of holographic models with broken translational invariance. We compute the transverse quasi-normal mode spectrum and the propagation speed of the lowest energy mode. We find that the speed of the lowest mode relates to the BH rigidity modulus as dictated by elasticity theory. This allows to identify these modes as transverse phonons---the pseudo Goldstone bosons of spontaneously broken translational invariance. In addition, we show that these modes have a mass gap controlled by an explicit source of the translational symmetry breaking. These results provide a new confirmation that the BHs in these models do exhibit solid properties that become more manifest at low temperatures. Also, by the AdS/CFT correspondence, this allows to extend the standard results from the effective field theory for solids to quantum-critical materials.Comment: 28 pages, 7 figures; v3: minor revisions, matching JHEP published versio

Holographic Phonons

We present a class of holographic massive gravity models that realize a spontaneous breaking of translational symmetry - they exhibit transverse phonon modes whose speed relates to the elastic shear modulus according to elasticity theory. Massive gravity theories thus emerge as versatile and convenient theories to model generic types of translational symmetry breaking: explicit, spontaneous and a mixture of both. The nature of the breaking is encoded in the radial dependence of the graviton mass. As an application of the model, we compute the temperature dependence of the shear modulus and find that it features a glass-like melting transition.Comment: 5+3 pages, 6 figure

Semiclassical Calculation of Multiparticle Scattering Cross Sections in Classicalizing Theories

It has been suggested in arXiv:1010.1415 that certain derivatively coupled non-renormalizable scalar field theories might restore the perturbative unitarity of high energy hard scatterings by classicalization, i.e. formation of multiparticle states of soft quanta. Here we apply the semiclassical method of calculating the multiparticle production rates to the scalar Dirac-Born-Infeld (DBI) theory which is suggested to classicalize. We find that the semiclassical method is applicable for the energies in the final state above the cutoff scale of the theory L_*^{-1}. We encounter that the cross section of the process two to N ceases to be exponentially suppressed for the particle number in the final state N smaller than a critical particle number N_{crit} ~ (E L_*)^{4/3}. It coincides with the typical particle number produced in two-particle collisions at high energies predicted by classicalization arguments.Comment: 17 pages, 4 figures, v2. Minor changes to match the published versio

Reduced Massive Gravity with Two St\"uckelberg Fields

We consider the non-linear massive gravity as a theory of a number of St\"uckelberg scalar fields minimally coupled to the Einstein-Hilbert gravity and argue that the counting of degrees of freedom can be done for scalar theory and gravity separately. In this paper we investigate the system with only two St\"uckelberg scalar fields. In this case we find the analytic expression for the determinant of the kinetic matrix of the scalar field Lagrangian and perform the full constraint analysis. In 1+1 space-time dimensions the theory corresponds to the full non-linear massive gravity, and this determinant vanishes identically. In this case we find two first-class constraints, and present the corresponding gauge symmetry of the theory which eliminates both scalar degrees of freedom. In 3+1 dimensions the determinant of the kinetic matrix does not vanish identically and, for generic initial conditions, both scalar fields are propagating.Comment: 21 pages, 1 figur