A New approach to integrable theories in any dimension

Oct, 1997
57 pages
Published in:
  • Nucl.Phys.B 529 (1998) 689-736
e-Print:
Report number:
  • US-FT-31-97,
  • IFT-P-066-97,
  • UMTG-202

Citations per year

19982005201220192024024681012
Abstract: (Elsevier)
The zero curvature representation for two-dimensional integrable models is generalized to spacetimes 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 C P 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 C P 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 2 j + l conserved currents leading to 2 j + 1 Lorentz scalar charges.
Note:
  • 52 pages, 4 figures, shortened version to appear in NPB
  • 11.15.Kc
  • 11.15.Tk
  • 11.30.Na
  • PACS: 11.10.Kk
  • Zero curvature
  • General dimensions
  • Integrability
  • New solutions
  • integrability
  • any-dimensional