# Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions

## Abstract

In this paper, the collective modes of an effective kinetic theory description based on the Boltzmann equation in a relaxation-time approximation applicable to gauge theories at weak but finite coupling and low frequencies are studied. Real time retarded two-point correlators of the energy-momentum tensor and the R-charge current are calculated at finite temperature in flat space-times for large N gauge theories. It is found that the real-time correlators possess logarithmic branch cuts which in the limit of large coupling disappear and give rise to non-hydrodynamic poles that are reminiscent of quasi-normal modes in black holes. In addition to branch cuts, correlators can have simple hydrodynamic poles, generalizing the concept of hydrodynamic modes to intermediate wavelength. Surprisingly, the hydrodynamic poles cease to exist for some critical value of the wavelength and coupling reminiscent of the properties of onset transitions.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1259198

- Alternate Identifier(s):
- OSTI ID: 1437933

- Grant/Contract Number:
- SC0008132

- Resource Type:
- Published Article

- Journal Name:
- European Physical Journal. C, Particles and Fields

- Additional Journal Information:
- Journal Name: European Physical Journal. C, Particles and Fields Journal Volume: 76 Journal Issue: 6; Journal ID: ISSN 1434-6044

- Publisher:
- Springer Science + Business Media

- Country of Publication:
- Germany

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Gauge Theory; Kinetic Theory; Hooft Coupling; Hydrodynamic Limit; Onset Transition

### Citation Formats

```
Romatschke, Paul. Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions. Germany: N. p., 2016.
Web. doi:10.1140/epjc/s10052-016-4169-7.
```

```
Romatschke, Paul. Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions. Germany. doi:10.1140/epjc/s10052-016-4169-7.
```

```
Romatschke, Paul. Fri .
"Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions". Germany. doi:10.1140/epjc/s10052-016-4169-7.
```

```
@article{osti_1259198,
```

title = {Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions},

author = {Romatschke, Paul},

abstractNote = {In this paper, the collective modes of an effective kinetic theory description based on the Boltzmann equation in a relaxation-time approximation applicable to gauge theories at weak but finite coupling and low frequencies are studied. Real time retarded two-point correlators of the energy-momentum tensor and the R-charge current are calculated at finite temperature in flat space-times for large N gauge theories. It is found that the real-time correlators possess logarithmic branch cuts which in the limit of large coupling disappear and give rise to non-hydrodynamic poles that are reminiscent of quasi-normal modes in black holes. In addition to branch cuts, correlators can have simple hydrodynamic poles, generalizing the concept of hydrodynamic modes to intermediate wavelength. Surprisingly, the hydrodynamic poles cease to exist for some critical value of the wavelength and coupling reminiscent of the properties of onset transitions.},

doi = {10.1140/epjc/s10052-016-4169-7},

journal = {European Physical Journal. C, Particles and Fields},

number = 6,

volume = 76,

place = {Germany},

year = {2016},

month = {6}

}

DOI: 10.1140/epjc/s10052-016-4169-7

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*upper left*), intermediate coupling (

*upper right and lower left*), and in the strong-coupling expansion (

*lower right*). Note that the hydrodynamic pole ceases to exist at weak coupling. See text for details

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Works referencing / citing this record:

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Do nuclear collisions create a locally equilibrated quark–gluon plasma?

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*