• DOI:10.1007/s00220-002-0734-z
• Corpus ID: 119547261

On Noncommutative Multi-Solitons

@article{Gopakumar2001OnNM,
  title={On Noncommutative Multi-Solitons},
  author={Rajesh Gopakumar and Matthew Headrick and Marcus Spradlin},
  journal={Communications in Mathematical Physics},
  year={2001},
  volume={233},
  pages={355-381}
}

• R. Gopakumar, M. Headrick, M. Spradlin
• Published 30 March 2001
• Mathematics
• Communications in Mathematical Physics

Abstract: We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a Kähler de-singularization of the symmetric product (ℝ2)k/Sk. We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ2/ℤk, cylinder, and T2. However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli space provides an explicit Kähler resolution of (ℝ4)k/Sk. In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂd, which for d>2 (and k>3) is not smooth and can have multiple branches.