# Analytic transport from weak to strong coupling in the $O\left(N\right)$ model

## Abstract

In this work, a second-order transport coefficient (the curvature-matter coupling $$\kappa$$) is calculated exactly for the O(N) model at large N for any coupling value. Since the theory is ``trivial'' in the sense of possessing a Landau pole, the result for $$\kappa$$ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with $$\phi^4$$ interaction.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1564538

- Alternate Identifier(s):
- OSTI ID: 1593883

- Grant/Contract Number:
- SC0017905

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Finite temperature field theory; Large-N expansion in field theory; Nonperturbative effects in field theory; Transport phenomena

### Citation Formats

```
Romatschke, Paul. Analytic transport from weak to strong coupling in the O ( N ) model. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.054029.
```

```
Romatschke, Paul. Analytic transport from weak to strong coupling in the O ( N ) model. United States. doi:10.1103/PhysRevD.100.054029.
```

```
Romatschke, Paul. Mon .
"Analytic transport from weak to strong coupling in the O ( N ) model". United States. doi:10.1103/PhysRevD.100.054029.
```

```
@article{osti_1564538,
```

title = {Analytic transport from weak to strong coupling in the O ( N ) model},

author = {Romatschke, Paul},

abstractNote = {In this work, a second-order transport coefficient (the curvature-matter coupling $\kappa$) is calculated exactly for the O(N) model at large N for any coupling value. Since the theory is ``trivial'' in the sense of possessing a Landau pole, the result for $\kappa$ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with $\phi^4$ interaction.},

doi = {10.1103/PhysRevD.100.054029},

journal = {Physical Review D},

number = 5,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}

DOI: 10.1103/PhysRevD.100.054029

*Citation information provided by*

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Web of Science

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