# Non-perturbative large N trans-series for the Gross–Witten–Wadia beta function

## Abstract

We describe the non-perturbative trans-series, at both weak- and strong-coupling, of the large N approximation to the beta function of the Gross–Witten–Wadia unitary matrix model. This system models a running coupling, and the structure of the trans-series changes as one crosses the large N phase transition. The perturbative beta function acquires a non-perturbative trans-series completion at large but finite N in the 't Hooft limit, as does the running coupling.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Connecticut, Storrs, CT (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1468371

- Alternate Identifier(s):
- OSTI ID: 1611396

- Grant/Contract Number:
- SC0010339

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 785 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics

### Citation Formats

```
Ahmed, Anees, and Dunne, Gerald V. Non-perturbative large N trans-series for the Gross–Witten–Wadia beta function. Netherlands: N. p., 2018.
Web. doi:10.1016/j.physletb.2018.08.072.
```

```
Ahmed, Anees, & Dunne, Gerald V. Non-perturbative large N trans-series for the Gross–Witten–Wadia beta function. Netherlands. doi:https://doi.org/10.1016/j.physletb.2018.08.072
```

```
Ahmed, Anees, and Dunne, Gerald V. Mon .
"Non-perturbative large N trans-series for the Gross–Witten–Wadia beta function". Netherlands. doi:https://doi.org/10.1016/j.physletb.2018.08.072.
```

```
@article{osti_1468371,
```

title = {Non-perturbative large N trans-series for the Gross–Witten–Wadia beta function},

author = {Ahmed, Anees and Dunne, Gerald V.},

abstractNote = {We describe the non-perturbative trans-series, at both weak- and strong-coupling, of the large N approximation to the beta function of the Gross–Witten–Wadia unitary matrix model. This system models a running coupling, and the structure of the trans-series changes as one crosses the large N phase transition. The perturbative beta function acquires a non-perturbative trans-series completion at large but finite N in the 't Hooft limit, as does the running coupling.},

doi = {10.1016/j.physletb.2018.08.072},

journal = {Physics Letters B},

number = C,

volume = 785,

place = {Netherlands},

year = {2018},

month = {10}

}

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DOI: https://doi.org/10.1016/j.physletb.2018.08.072

DOI: https://doi.org/10.1016/j.physletb.2018.08.072

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