Integrable Noncommutative Sine-Gordon Model
arXiv:hep-th/0406065 · doi:10.1016/j.nuclphysb.2004.10.050
Abstract
Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, 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, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2)->U(1) to U(2)->U(1)xU(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.
1+23 pages (+27 eps figs)
References in corpus (1)
Cited by in corpus (27)
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- Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations
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