Topological hydrodynamic modes and holography

TL;DR

This paper investigates topological features in relativistic hydrodynamics, revealing nontrivial crossing nodes protected by symmetries, and proposes a holographic model to analyze these phenomena.

Contribution

It introduces the concept of topological hydrodynamic modes with symmetry protection and presents a novel holographic approach to study their properties.

Findings

Identification of topologically nontrivial crossing nodes in hydrodynamic spectra

Confirmation of topology via topological invariants

Proposal of a holographic realization and a new method for Ward identity calculations

Abstract

We study topological modes in relativistic hydrodynamics by weakly breaking the conservation of energy momentum tensor. Several systems have been found to have topologically nontrivial crossing nodes in the spectrum of hydrodynamic modes and some of them are only topologically nontrivial with the protection of reflection symmetries in two directions. The nontrivial topology for all these systems is further confirmed from a calculation of the topological invariant. Associated transport properties and second order effects have also been studied for these systems. The non-conservation terms of the energy momentum tensor could come from an external effective symmetric tensor matter field or a gravitational field which could be generated by a specific non-inertial reference frame transformation from the original inertial reference frame. Finally we introduce a possible holographic realization of one of these systems. We propose a new method to calculate the holographic Ward identities for the energy momentum tensor without calculating out all components of the Green functions and match the Ward identities of both sides.