# Thermalization and Hydrodynamics of Two-Dimensional Quantum Field Theories

### Submission summary

 As Contributors: Luca Delacrétaz Arxiv Link: https://arxiv.org/abs/2105.02229v1 (pdf) Date submitted: 2021-05-17 00:31 Submitted by: Delacrétaz, Luca Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

### Abstract

We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the temperature and the scale associated with the relevant deformation. This bound is typically much stronger than $\frac{1}{T}$, the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic $C$-function, and constrain the sign of the $\mathcal T\bar{\mathcal T}$ term in EFTs.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

#### Published as SciPost Phys. 12, 119 (2022)

Resubmission 2105.02229v3 on 4 February 2022
Resubmission 2105.02229v2 on 8 September 2021

Submission 2105.02229v1 on 17 May 2021

## Reports on this Submission

### Anonymous Report 1 on 2021-7-1 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2105.02229v1, delivered 2021-07-01, doi: 10.21468/SciPost.Report.3154

### Report

This paper adds to the list of recent investigations regarding bounds on characteristics of thermal quantum many-body systems based on fundamental QFT principles. The authors investigate the onset time after which only excitations of conserved quantities are important in relevant deformations of thermal CFTs. The lower bound for this hydrodynamic "equilibration time" puts a fundamental constraint on thermalization. It depends on the diffusion constant as it relies on balancing causality of the QFT against superluminality of diffusive hydrodynamics at very early times.

At a technical level, the analysis relies on conformal perturbation theory around the UV CFT (e.g. to obtain a correction to the conformal equation of state). Several extensions (such as higher dimensions, additional symmetries etc.) as well as specific examples (such as free fields and integrable flows) are discussed.

The content is original, should be of interest to the community, and seems to be correct. The paper is comprehensive, very well written, and nicely structured. Figures are clear and helpful. I recommend publication basically as is. My only suggestion would be to make some parts of the manuscript a bit more easily accessible. As it is written, the content is sometimes quite dense and perhaps not always easy to follow for a more "casual" reader. To give two specific examples: I found the reasoning around Eqs. (8), (9) and (47) a bit hard to digest unless one is already intimately familiar with it. I will consider this suggestion as optional for the authors to take into account, as it will merely improve readability for a certain audience, but is not strictly necessary from a scientific point of view.

• validity: high
• significance: high
• originality: high
• clarity: ok
• formatting: perfect
• grammar: perfect

### Author:  Luca Delacrétaz  on 2021-09-07  [id 1741]

(in reply to Report 1 on 2021-07-01)

We thank the referee for the positive feedback. Following their suggestions, we have added several comments in the v2 to guide the more casual reader.

In the interest of the reader, we would like to clarify that our bound does not depend on the diffusion constant -- the equilibration time is lower bounded by entirely thermodynamic quantities. This arises because of the large hydrodynamic fluctuations in (1+1)d.