Abstract
The sine-Gordon model may be obtained by dimensional and algebraic reduction from (2+2)-dimensional self-dual U(2) Yang-Mills through a (2+1)-dimensional integrable U(2) sigma model. It is argued that the noncommutative (Moyal) deformation of this procedure should relax the algebraic reduction from U(2) → U(1) to U(2)→U(1) × U(1). The result are novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is outlined for constructing its multi-soliton solutions. Finally, the tree-level amplitudes demonstrate that this model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.
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Lechtenfeld, O. Noncommutative Sine-Gordon Model. Czech J Phys 54, 1351–1357 (2004). https://doi.org/10.1007/s10582-004-9800-4
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DOI: https://doi.org/10.1007/s10582-004-9800-4