# Viscoelastic hydrodynamics and holography

## TL;DR

This paper develops a comprehensive theoretical framework for nonlinear viscoelastic hydrodynamics in anisotropic crystals, incorporating dissipative effects, and establishes a dual holographic description with a new model proposal.

## Contribution

It introduces a novel formulation of viscoelastic hydrodynamics using Goldstone scalars and higher-form superfluids, and connects these with holographic models through boundary condition analysis.

## Key findings

- Formulated nonlinear viscoelastic hydrodynamics with dissipative effects.
- Established an exact map between different formulations of viscoelastic hydrodynamics.
- Proposed a new holographic model with alternative scalar quantisation.

## 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.