# Self-duality for SU([infinity]) gauge theories and extended objects

## Abstract

The main theme of this thesis is the formulation of self-duality for extended objects (p-branes). An approach to self-duality for membranes is developed using the correspondence between the large N limit of SU(N) gauge theories and the membrane theory. This correspondence is established via the use of the coadjoint orbit method. It is shown that classical gauge field theories can be formulated on the coadjoint orbits of an infinite dimensional group (a semidirect product of the group of gauge transformations and the Heisenberg-Weyl group); in Chap. II this construction is carried out for Yang-Mills, Cherns-Simons, topological Yang-Mills and F B theories, as well as the Wess-Zumino-Novikov-Witten model. In Chap. III it is shown that for homogeneous fields (i.e. gauge mechanics) and in the N [yields] [infinity] limit, the coadjoint orbit action becomes identical to the membrane action in the light cone gauge. The self-duality equations for gauge fields then translate into the self-duality equations for membranes. In Chap. IV another approach is developed, one which allows us to formulate the self-duality equations for a much larger class of extended objects. This generalized self-duality is based on the notion of p-fold vector products. The author exhibits several classes of solutions formore »

- Authors:

- Publication Date:

- Research Org.:
- Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States)

- OSTI Identifier:
- 5638692

- Resource Type:
- Miscellaneous

- Resource Relation:
- Other Information: Thesis (Ph.D.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; EXTENDED PARTICLE MODEL; MANY-DIMENSIONAL CALCULATIONS; FIELD THEORIES; GAUGE INVARIANCE; DUALITY; LIGHT CONE; MEMBRANES; YANG-MILLS THEORY; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; PARTICLE MODELS; SPACE-TIME; 662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)

### Citation Formats

```
Grabowski, M P.
```*Self-duality for SU([infinity]) gauge theories and extended objects*. United States: N. p., 1992.
Web.

```
Grabowski, M P.
```*Self-duality for SU([infinity]) gauge theories and extended objects*. United States.

```
Grabowski, M P. Wed .
"Self-duality for SU([infinity]) gauge theories and extended objects". United States.
```

```
@article{osti_5638692,
```

title = {Self-duality for SU([infinity]) gauge theories and extended objects},

author = {Grabowski, M P},

abstractNote = {The main theme of this thesis is the formulation of self-duality for extended objects (p-branes). An approach to self-duality for membranes is developed using the correspondence between the large N limit of SU(N) gauge theories and the membrane theory. This correspondence is established via the use of the coadjoint orbit method. It is shown that classical gauge field theories can be formulated on the coadjoint orbits of an infinite dimensional group (a semidirect product of the group of gauge transformations and the Heisenberg-Weyl group); in Chap. II this construction is carried out for Yang-Mills, Cherns-Simons, topological Yang-Mills and F B theories, as well as the Wess-Zumino-Novikov-Witten model. In Chap. III it is shown that for homogeneous fields (i.e. gauge mechanics) and in the N [yields] [infinity] limit, the coadjoint orbit action becomes identical to the membrane action in the light cone gauge. The self-duality equations for gauge fields then translate into the self-duality equations for membranes. In Chap. IV another approach is developed, one which allows us to formulate the self-duality equations for a much larger class of extended objects. This generalized self-duality is based on the notion of p-fold vector products. The author exhibits several classes of solutions for these generalized self-dual extended objects and classify all the cases in which they exist. It is shown that the self-intersecting string instantons, introduced by Polyakov constitute a special case of these solutions. Of particular interest are two octonionic classes: A membrane in 7 dimensions and a 3-brane in 8 dimensions. To simplify the calculations in these cases an approach to octonionic symbolic computing making use of [open quotes]Mathematica[close quotes] was developed. Some possible applications of self-dual extended objects are briefly discussed.},

doi = {},

url = {https://www.osti.gov/biblio/5638692},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1992},

month = {1}

}