Noncommutative solitons and closed string tachyons.

摘要

In the first part of this thesis, we find the moduli space of multi-solitons in noncommutative scalar field theories at large &thetas;, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/&thetas; is a consequence of a Bogomolnyi bound obeyed by the kinetic energy of the &thetas; = ∞ solitons. In two spatial dimensions, the parameter space for k solitons is a Kähler de-singularization of the symmetric product /S_k. 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 2π&thetas; do not admit stable solitons. In four dimensions the moduli space provides an explicit Kähler resolution of /S_k. In general spatial dimension 2 d, 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. We also study multi-solitons on the fuzzy sphere and fuzzy hyperbolic plane, finding an effective potential on the moduli space depending on the curvature.; In the second part of this thesis, we study renormalization group flows in unitary two dimensional sigma models with asymptotically flat target spaces. Applying an infrared cutoff to the target space, we use the Zamolodchikov c-theorem to demonstrate that the target space ADM energy of the UV fixed point is greater than that of the IR fixed point: spacetime energy decreases under world-sheet RG flow. This result mirrors the well understood decrease of spacetime Bondi energy in the time evolution process of tachyon condensation.