### Abstract

The zero curvature representation for two-dimensional integrable models is generalized to space-times of dimension d + 1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2 + 1 dimensions (BF theories, Chern-Simons, 2+1 gravity and the ℂP^{1} model) and 3 + 1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2 + 1-dimensional ℂP^{1} model, we explicitly construct an infinite number of previously unknown non-trivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j + 1 conserved currents leading to 2j + 1 Lorentz scalar charges.

Original language | English (US) |
---|---|

Pages (from-to) | 689-736 |

Number of pages | 48 |

Journal | Nuclear Physics B |

Volume | 529 |

Issue number | 3 |

State | Published - Oct 5 1998 |

### Fingerprint

### Keywords

- General dimensions
- Integrability
- New solutions
- Zero curvature

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*529*(3), 689-736.

**A new approach to integrable theories in any dimension.** / Alvarez, Orlando; Ferreira, Luiz A.; Guillén, J. Sánchez.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 529, no. 3, pp. 689-736.

}

TY - JOUR

T1 - A new approach to integrable theories in any dimension

AU - Alvarez, Orlando

AU - Ferreira, Luiz A.

AU - Guillén, J. Sánchez

PY - 1998/10/5

Y1 - 1998/10/5

N2 - The zero curvature representation for two-dimensional integrable models is generalized to space-times of dimension d + 1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2 + 1 dimensions (BF theories, Chern-Simons, 2+1 gravity and the ℂP1 model) and 3 + 1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2 + 1-dimensional ℂP1 model, we explicitly construct an infinite number of previously unknown non-trivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j + 1 conserved currents leading to 2j + 1 Lorentz scalar charges.

AB - The zero curvature representation for two-dimensional integrable models is generalized to space-times of dimension d + 1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2 + 1 dimensions (BF theories, Chern-Simons, 2+1 gravity and the ℂP1 model) and 3 + 1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2 + 1-dimensional ℂP1 model, we explicitly construct an infinite number of previously unknown non-trivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j + 1 conserved currents leading to 2j + 1 Lorentz scalar charges.

KW - General dimensions

KW - Integrability

KW - New solutions

KW - Zero curvature

UR - http://www.scopus.com/inward/record.url?scp=0032487309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032487309&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032487309

VL - 529

SP - 689

EP - 736

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -