The Decay of Unstable Noncommutative Solitons

Details The Decay of Unstable Noncommutative Solitons The Decay of Unstable Noncommutative Solitons

2003-01-17

arxiv.org/abs/hep-th/0301119v2

Commun.Math.Phys. 237 (2003) 243-269

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, 7 figures, dedicated to Rudolf Haag. v2: uniform estimate for Weyl criterion provided, refs added

Scientific paper

10.1007/s00220-003-0863-z

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.

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