On noncommultative multi-solitons

We find the moduli space of multi-solitons in noncommutative scalar field theories at large 0, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/theta is a consequence of a Bogomolnyi. bound obeyed by the kinetic energy of the theta = infinity solitons. In two spatial dimensions, the parameter space for k solitons is a Kahler de-singularization of the symmetric product (R-2)(k)/S-k. We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: R-2/Z(k), cylinder, and T-2. However, we show that tori of area less than or equal to 2pitheta do not admit stable solitons. In four dimensions the moduli space provides an explicit Kahler resolution of (R-4)(k)/S-k. In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in C-d, which for d > 2 (and k > 3) is not smooth and can have multiple branches.