Viscoelastic hydrodynamics and holography

Abstract

We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of plastic deformations. We reformulate classical elasticity effective field theory using surface calculus in which the Goldstone scalars naturally define the position of higher-dimensional crystal cores, covering both elastic and smectic crystal phases. We systematically incorporate all dissipative effects in viscoelastic hydrodynamics at first order in a long-wavelength expansion and study the resulting rheology equations. In the process, we find the necessary conditions for equilibrium states of viscoelastic materials. In the linear regime and for isotropic crystals, the theory includes the description of Kelvin-Voigt materials. Furthermore, we provide an entirely equivalent description of viscoelastic hydrodynamics as a novel theory of higher-form superfluids in arbitrary dimensions where the Goldstone scalars of partially broken generalised global symmetries play an essential role. An exact map between the two formulations of viscoelastic hydrodynamics is given. Finally, we study holographic models dual to both these formulations and map them one-to-one via a careful analysis of boundary conditions. We propose a new simple holographic model of viscoelastic hydrodynamics by adopting an alternative quantisation for the scalar fields.

Superfluids as higher-form anomalies

“…The ideas discussed here are in line with recent progress in incorporating higher form symmetries in hydrodynamics [8,7,40,36,41,37,42] and we expect to see further developments in this area.…”

“…In this case one needs to consider more general volume preserving deformations of the fluid element, not present for the 0-form case. These are important in the theory of elasticity and have been considered in a modern setup recently in [37]. expressions 13 ǫ + p = sT + ρµ +ρ μ +ρ ⊥μ⊥ , (4.15)…”

Gapless and gapped holographic phonons

“…Some disagreement in holographic massive gravity models has been reported [46]. On the other hand, [48] recently carried out a careful analysis of the dispersion relation of the modes with a nonzero background strain, and find new contributions in the longitudinal sector, which may resolve this discrepancy. 10 Finally, the universal relation (4.5) remains to be tested more generally, in other holographic models of spontaneous translation symmetry breaking, homogeneous or not [19,35,42], in particular for thermodynamically stable phases, or directly in field theory.…”

“…[46] finds a discrepancy between the hydrodynamic prediction in the longitudinal sector and the holographic result, which is not resolved at this point. It is likely though that a resolution lies in a proper accounting of the background strain of these phases, along the lines explained in [48]. This sources new contributions in the dispersion relations of the longitudinal modes.…”

Scale invariant solids

“…More precisely, it is valid only for the standard quantization case, in which the leading term of the expansion is identified with the source of the dual operator and the subleading term with its VEV. By changing the boundary conditions, via a double trace deformation, it is possible to achieve the SSB of translations for any potential V[36].…”