Comment on "Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory".

Abstract

We discuss a field-theoretical approach to liquids, solids, and glasses, published recently [Phys. Rev. E 105, 034108 (2022)10.1103/PhysRevE.105.034108], which aims to describe these materials in a common formalism. We argue that such a formalism contradicts the known hydrodynamic theory of classical liquids. In particular, the authors miss the important particle-number conservation law and the density fluctuations as a hydrodynamic slow variable. This results in an exotic mechanism of hydrodynamic sound instead of the standard hydrodynamic one due to combined particle-number and momentum conservation, a fact well documented in fluid-mechanics textbooks.