# Convergence of hydrodynamic modes: insights from kinetic theory and holography

### Submission summary

 Authors (as Contributors): Michal P. Heller · Alexandre Serantes · Benjamin Withers
Submission information
Arxiv Link: https://arxiv.org/abs/2012.15393v1 (pdf)
Date accepted: 2021-05-26
Date submitted: 2021-02-04 17:22
Submitted by: Serantes, Alexandre
Submitted to: SciPost Physics
Ontological classification
Specialties:
• High-Energy Physics - Theory
• Nuclear Physics - Theory
Approach: Theoretical

### Abstract

We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More generally, we examine the consequences of the implicit function theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.

Published as SciPost Phys. 10, 123 (2021)

### Submission & Refereeing History

Submission 2012.15393v1 on 4 February 2021

## Reports on this Submission

### Anonymous Report 1 on 2021-3-11 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2012.15393v1, delivered 2021-03-11, doi: 10.21468/SciPost.Report.2681

### Strengths

1- very well written, clear structure
2- results are new and timely
3- discussion of results is sufficiently detailed, but always to the point

### Report

The authors consider hydrodynamic shear and sound dispersion relations $\omega = \omega(k)$ and study the radius of convergence of the expansion around $k=0$ using kinetic theory (weak coupling). In the relaxation time approximation, the relevant retarded Green's functions are known explicitly and have poles as well as branch points. The paper provides evidence that the radius of convergence of the hydrodynamic expansion is given by the location where hydrodynamic poles collide with the logarithmic branch point or a pole on the second sheet of the retarded Green's function. The evidence is mostly numerical. The numerical results are convincing (the authors provide detailed consistency checks) and appear to be correct.

The paper is very well written and structured, explanations are clear, detailed and thorough. The results are new and timely, making contact with numerous recent developments on the convergence of the hydrodynamic expansion in holography (and MIS theory) and offering novel viewpoints.

Regarding SciPost's acceptance criteria: while the content of the paper may not be groundbreaking, I think it does "provide a novel and synergetic link between different research areas" by establishing interesting connections and contrasts between strongly vs. weakly coupled hydrodynamics, while also offering some conjectures and open questions for future research. All general acceptance criteria are met as far as I can tell. I would recommend the paper for publication as is.

• validity: top
• significance: good
• originality: good
• clarity: top
• formatting: excellent
• grammar: perfect