# The algebras of large N matrix mechanics

## Abstract

Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Director. Office of Energy Research. Office of Basic Energy Sciences; National Science Foundation Grant PHY-95-14797 (US)

- OSTI Identifier:
- 836360

- Report Number(s):
- LBNL-42212

R&D Project: PTHOPS; TRN: US0500565

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Journal Article

- Journal Name:
- Inaternational Journal of Modern Physics A

- Additional Journal Information:
- Journal Volume: 14; Journal Issue: 19; Other Information: Submitted to International Journal of Modern Physics A: Volume 14, No.19; Journal Publication Date: 07/30/1999; PBD: 16 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HAMILTONIANS; SUPERSYMMETRY; LAWRENCE BERKELEY LABORATORY

### Citation Formats

```
Halpern, M.B., and Schwartz, C.
```*The algebras of large N matrix mechanics*. United States: N. p., 1999.
Web. doi:10.1142/S0217751X99001482.

```
Halpern, M.B., & Schwartz, C.
```*The algebras of large N matrix mechanics*. United States. doi:10.1142/S0217751X99001482.

```
Halpern, M.B., and Schwartz, C. Thu .
"The algebras of large N matrix mechanics". United States. doi:10.1142/S0217751X99001482. https://www.osti.gov/servlets/purl/836360.
```

```
@article{osti_836360,
```

title = {The algebras of large N matrix mechanics},

author = {Halpern, M.B. and Schwartz, C.},

abstractNote = {Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.},

doi = {10.1142/S0217751X99001482},

journal = {Inaternational Journal of Modern Physics A},

number = 19,

volume = 14,

place = {United States},

year = {1999},

month = {9}

}