A New approach to integrable theories in any dimension
Oct, 1997
57 pages
Published in:
- Nucl.Phys.B 529 (1998) 689-736
e-Print:
- hep-th/9710147 [hep-th]
Report number:
- US-FT-31-97,
- IFT-P-066-97,
- UMTG-202
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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
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