# One-loop structure of higher rank Wilson loops in AdS/CFT

## Abstract

The half-supersymmetric Wilson loop in N=4 SYM is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of SU(N) are captured to all orders in perturbation theory by a Gaussian matrix model. Of prominent interest are the k-symmetric and k-antisymmetric representations, whose gravitational description is given in terms of D3- and D5-branes, respectively, with fluxes in their world volumes. At leading order in N and λ the agreement in both cases is exact. In this work, we explore the structure of the next-to-leading order correction in the matrix model and compare with existing string theory calculations. We find agreement in the functional dependence on k but a mismatch in the numerical coefficients.

- Authors:

- Pontifical Catholic Univ. of Chile, Santiago (Chile). Inst. of Physics
- Univ. of Michigan, Ann Arbor, MI (United States). Michigan Center for Theoretical Physics
- Univ. of Science and Technology of China, Hefei (China). Dept. of Modern Physics

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC); National Commission of Scientific and Technological Research (CONICYT) (Chile); Sao Paulo Research Foundation (FAPESP) (Brazil); Univ. of Sao Paulo (Brazil)

- OSTI Identifier:
- 1198347

- Alternate Identifier(s):
- OSTI ID: 1454571

- Grant/Contract Number:
- SC0007859; 821320022; 2012/03437-8

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physics Letters. Section B

- Additional Journal Information:
- Journal Volume: 740; Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Faraggi, Alberto, Liu, James T., Pando Zayas, Leopoldo A., and Zhang, Guojun.
```*One-loop structure of higher rank Wilson loops in AdS/CFT*. United States: N. p., 2014.
Web. doi:10.1016/j.physletb.2014.11.060.

```
Faraggi, Alberto, Liu, James T., Pando Zayas, Leopoldo A., & Zhang, Guojun.
```*One-loop structure of higher rank Wilson loops in AdS/CFT*. United States. doi:10.1016/j.physletb.2014.11.060.

```
Faraggi, Alberto, Liu, James T., Pando Zayas, Leopoldo A., and Zhang, Guojun. Thu .
"One-loop structure of higher rank Wilson loops in AdS/CFT". United States.
doi:10.1016/j.physletb.2014.11.060.
```

```
@article{osti_1198347,
```

title = {One-loop structure of higher rank Wilson loops in AdS/CFT},

author = {Faraggi, Alberto and Liu, James T. and Pando Zayas, Leopoldo A. and Zhang, Guojun},

abstractNote = {The half-supersymmetric Wilson loop in N=4 SYM is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of SU(N) are captured to all orders in perturbation theory by a Gaussian matrix model. Of prominent interest are the k-symmetric and k-antisymmetric representations, whose gravitational description is given in terms of D3- and D5-branes, respectively, with fluxes in their world volumes. At leading order in N and λ the agreement in both cases is exact. In this work, we explore the structure of the next-to-leading order correction in the matrix model and compare with existing string theory calculations. We find agreement in the functional dependence on k but a mismatch in the numerical coefficients.},

doi = {10.1016/j.physletb.2014.11.060},

journal = {Physics Letters. Section B},

number = C,

volume = 740,

place = {United States},

year = {Thu Dec 04 00:00:00 EST 2014},

month = {Thu Dec 04 00:00:00 EST 2014}

}

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