# Wilson loops in minimal surfaces

## Abstract

The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N = 4 supersymmetry in 4 dimensions is described by a minimal surface in AdS{sub 5} x S{sup 5}. The authors examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which the authors call BPS loops, whose expectation values are free from ultra-violet divergence. They formulate the loop equation for such loops. To the extent that they have checked, the minimal surface in AdS{sub 5} x S{sup 5} gives a solution of the equation. The authors also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory, they expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. They will show how this is realized for the minimal surface.

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US) (US)

- Sponsoring Org.:
- USDOE Director, Office of Science. Office of High Energy and Nuclear Physics (US)

- OSTI Identifier:
- 753038

- Report Number(s):
- LBNL-43079; UCB-PTH-99/11; NSF-ITP-99-22; hep-th/9904191

R&D Project: 417001; TRN: US0003741

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 27 Apr 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; WILSON LOOP; GAUGE INVARIANCE; SUPERSYMMETRY; DIMENSIONS; SYMMETRY; QUANTUM FIELD THEORY

### Citation Formats

```
Drukker, Nadav, Gross, David J, and Ooguri, Hirosi.
```*Wilson loops in minimal surfaces*. United States: N. p., 1999.
Web. doi:10.2172/753038.

```
Drukker, Nadav, Gross, David J, & Ooguri, Hirosi.
```*Wilson loops in minimal surfaces*. United States. doi:10.2172/753038.

```
Drukker, Nadav, Gross, David J, and Ooguri, Hirosi. Tue .
"Wilson loops in minimal surfaces". United States. doi:10.2172/753038. https://www.osti.gov/servlets/purl/753038.
```

```
@article{osti_753038,
```

title = {Wilson loops in minimal surfaces},

author = {Drukker, Nadav and Gross, David J and Ooguri, Hirosi},

abstractNote = {The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N = 4 supersymmetry in 4 dimensions is described by a minimal surface in AdS{sub 5} x S{sup 5}. The authors examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which the authors call BPS loops, whose expectation values are free from ultra-violet divergence. They formulate the loop equation for such loops. To the extent that they have checked, the minimal surface in AdS{sub 5} x S{sup 5} gives a solution of the equation. The authors also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory, they expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. They will show how this is realized for the minimal surface.},

doi = {10.2172/753038},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {4}

}