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Solitons in 4d Wess-Zumino-Witten models -- Towards unification of integrable systems --
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We construct soliton solutions of the four-dimensional Wess-Zumino-Witten (4dWZW) model in the context of a unified theory of integrable systems with relation to the 4d/6d Chern-Simons theory. We calculate the action density of the solutions and find that the soliton solutions behave as the KP-type solitons, that is, the one-soliton solution has a localized action/energy density on a 3d hyperplane in 4-dimensions (soliton wall) and the n-soliton solution describes n intersecting soliton walls with phase shifts. We note that the Ward conjecture holds mostly in the split signature (+,+,-,-). Furthermore, the 4dWZW model describes the string field theory action of the open N=2 string theory in the four-dimensional space-time with the split signature and hence our soliton solutions would describe a new-type of physical objects in the N=2 string theory. We discuss instanton solutions in the 4dWZW model as well. Noncommutative extension and quantization of the unified theory of integrable systems are also discussed.
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Cited by 2 Pith papers
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Asymptotic Equivalence Between Quasi-Grammian and Quasi-Wronskian $N$-Soliton Solutions of the Anti-Self-Dual Yang-Mills Equation
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Soliton Resonances in Four Dimensional Wess-Zumino-Witten Model
Double-pole and V-shape resonance soliton solutions are constructed for the U(2) Yang equation on ultrahyperbolic space, with action densities that match known one- and two-soliton results and suggest new building blo...
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