# Comments on higher rank Wilson loops in $$\mathcal{N}$$ = 2*

## Abstract

For N = 2* theory with U(N) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigenvalue distributions in various regimes of parameters (N, λ, n, k) where λ is the ’t Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discuss the N = 4 limit of the N = 2* theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. Finally, as a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.

- Authors:

- Univ. of Michigan, Ann Arbor, MI (United States). Leinweber Center for Theoretical Physics, Randall Lab. of Physics
- Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
- Tsinghua Univ., Beijing (China). Inst. for Interdisciplinary Information Science

- Publication Date:

- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)

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

- OSTI Identifier:
- 1457339

- Grant/Contract Number:
- SC0017808; SC0007859

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N Expansion; Wilson; ’t Hooft and Polyakov loops; AdS-CFT Correspondence

### Citation Formats

```
Liu, James T., Zayas, Leopoldo A. Pando, and Zhou, Shan.
```*Comments on higher rank Wilson loops in $\mathcal{N}$ = 2**. United States: N. p., 2018.
Web. doi:10.1007/JHEP01(2018)047.

```
Liu, James T., Zayas, Leopoldo A. Pando, & Zhou, Shan.
```*Comments on higher rank Wilson loops in $\mathcal{N}$ = 2**. United States. doi:10.1007/JHEP01(2018)047.

```
Liu, James T., Zayas, Leopoldo A. Pando, and Zhou, Shan. Thu .
"Comments on higher rank Wilson loops in $\mathcal{N}$ = 2*". United States.
doi:10.1007/JHEP01(2018)047. https://www.osti.gov/servlets/purl/1457339.
```

```
@article{osti_1457339,
```

title = {Comments on higher rank Wilson loops in $\mathcal{N}$ = 2*},

author = {Liu, James T. and Zayas, Leopoldo A. Pando and Zhou, Shan},

abstractNote = {For N = 2* theory with U(N) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigenvalue distributions in various regimes of parameters (N, λ, n, k) where λ is the ’t Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discuss the N = 4 limit of the N = 2* theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. Finally, as a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.},

doi = {10.1007/JHEP01(2018)047},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2018,

place = {United States},

year = {Thu Jan 11 00:00:00 EST 2018},

month = {Thu Jan 11 00:00:00 EST 2018}

}

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