## The decay of unstable noncommutative solitons.(English)Zbl 1037.81094

Summary: We study the classical decay of unstable scalar solitons in noncommutative field theory in $$2+1$$ dimensions. This can, but does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the noncommutativity parameter $$\theta$$ is infinite, the gradient term is absent, there are no propagating modes and the soliton does not decay at all. If $$\theta$$ is large, but finite, the rotationally symmetric decay channel can be described as a highly excited nonlinear oscillator weakly coupled to a continuum of linear modes. This system is closely akin to those studied in the context of discrete breathers. We here diagonalize the linear problem and compute the decay rate to first order using a version of Fermi’s Golden Rule, leaving a more rigorous treatment for future work.

### MSC:

 81T75 Noncommutative geometry methods in quantum field theory 35B41 Attractors 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 83E30 String and superstring theories in gravitational theory 35Q51 Soliton equations
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