# 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:

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

- 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:
- Journal Article: Published Article

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

- Additional Journal Information:
- Journal Volume: 76; Journal Issue: 6; Journal ID: ISSN 1434-6044

- Publisher:
- Springer

- Country of Publication:
- United States

- 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*. United States: 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*. United States. doi:10.1140/epjc/s10052-016-4169-7.

```
Romatschke, Paul. Fri .
"Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions". United States.
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 = {United States},

year = {Fri Jun 24 00:00:00 EDT 2016},

month = {Fri Jun 24 00:00:00 EDT 2016}

}

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