A new approach to integrable theories in any dimension

Orlando Alvarez, Luiz A. Ferreira, J. Sánchez Guillén

Research output: Contribution to journalArticle

88 Citations (Scopus)

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 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.

Original languageEnglish (US)
Pages (from-to)689-736
Number of pages48
JournalNuclear Physics B
Volume529
Issue number3
StatePublished - Oct 5 1998

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curvature
Yang-Mills theory
two dimensional models
integers
equations of motion
gravitation
scalars

Keywords

  • General dimensions
  • Integrability
  • New solutions
  • Zero curvature

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Alvarez, O., Ferreira, L. A., & Guillén, J. S. (1998). A new approach to integrable theories in any dimension. Nuclear Physics B, 529(3), 689-736.

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

In: Nuclear Physics B, Vol. 529, No. 3, 05.10.1998, p. 689-736.

Research output: Contribution to journalArticle

Alvarez, O, Ferreira, LA & Guillén, JS 1998, 'A new approach to integrable theories in any dimension', Nuclear Physics B, vol. 529, no. 3, pp. 689-736.
Alvarez O, Ferreira LA, Guillén JS. A new approach to integrable theories in any dimension. Nuclear Physics B. 1998 Oct 5;529(3):689-736.
Alvarez, Orlando ; Ferreira, Luiz A. ; Guillén, J. Sánchez. / A new approach to integrable theories in any dimension. In: Nuclear Physics B. 1998 ; Vol. 529, No. 3. pp. 689-736.
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