Noncommutative Solitons: Moduli Spaces, Quantization, Finite Theta Effects and Stability

Abstract

We find the N-soliton solution at infinite theta, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading 1/theta corrections, and find an effective short range attraction between solitons. We study the stability of various solutions. We discuss the finite theta corrections to scattering, and find metastable orbits. Upon quantization of the two-soliton moduli space, for any finite theta, we find an s-wave bound state.

Second revision: Discussions of translation zero-modes in section 4 and scales in section 5 improved; web addresses of movies changed. First revision: Section 6 is rewritten (thanks to M. Headrick for pointing out a mistake in the original version); some references and acknowledgements added. 21 pages, JHEP style, Hypertex, 1 figure, 3 MPEG's at: http://www.physto.se/~unge/traj1.mpg http://www.physto.se/~unge/traj2.mpg http://www.physto.se/~unge/traj3.mpg