Scalar Multi-Solitons on the Fuzzy Sphere

Abstract

We study solitons in scalar theories with polynomial interactions on the fuzzy sphere. Such solitons are described by projection operators of rank k, and hence the moduli space for the solitons is the Grassmannian Gr(k,2j+1). The gradient term of the action provides a non-trivial potential on Gr(k,2j+1), thus reducing the moduli space. We construct configurations corresponding to well-separated solitons, and show that although the solitons attract each other, the attraction vanishes in the limit of large j. In this limit, it is argued that the moduli space is CP^k. For the k-soliton bound state, the moduli space is simply CP^1, all other moduli being lifted. We find that the moduli space of multi-solitons is smooth and that there are no singularities as several solitons coalesce. When the fuzzy S^2 is flattened to a noncommutative plane, we find agreement with the known results, modulo some operator-ordering ambiguities. This suggests that the fuzzy sphere is a natural way to regulate the noncommutative plane both in the ultraviolet and infrared.

13 pages LaTex, 5 figures. Typos corrected, some remarks added

References in corpus (6)

• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Scaling Limits of the Fuzzy Sphere at one Loop
• Perturbative dynamics on fuzzy S^2 and RP^2
• Projectors for the fuzzy sphere
• Noncommutative Solitons: Moduli Spaces, Quantization, Finite Theta Effects and Stability
• The Stability of Noncommutative Scalar Solitons

Cited by in corpus (9)

• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• A matrix phase for the phi^4 scalar field on the fuzzy sphere
• 2D fuzzy Anti-de Sitter space from matrix models
• A quantum algebraic description of D-branes on group manifolds
• A New Class of Two-Dimensional Noncommutative Spaces
• O(3) Sigma model with Hopf term on Fuzzy Sphere
• Scalar Solitons on the Fuzzy Sphere
• Quantum Entropy for the Fuzzy Sphere and its Monopoles
• Monopoles On $S_F^2$ From The Fuzzy Conifold